skomam2.mw

> taylor(sqrt(x),x=1,15);
 

series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1... 

> T15:=x->1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1)^12+52003/8388608*(x-1)^13-185725/33554432*(x-1)^14;
 

(Typesetting:-mprintslash)([T15 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T15 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T15 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T15 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T15 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-... 

> evalf(sqrt(2)-T15(2));
 

0.2617055e-2 

> taylor(sqrt(x),x=1,25);
 

series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1... 

> T25:=x->1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1)^12+52003/8388608*(x-1)^13-185725/33554432*(x-1)^14+334305/67108864*(x-1)^15-9694845/2147483648*(x-1)^16+17678835/4294967296*(x-1)^17-64822395/17179869184*(x-1)^18+119409675/34359738368*(x-1)^19-883631595/274877906944*(x-1)^20+1641030105/549755813888*(x-1)^21-6116566755/2199023255552*(x-1)^22+11435320455/4398046511104*(x-1)^23-171529806825/70368744177664*(x-1)^24;
 

(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T25 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-... 

> evalf(sqrt(2)-T25(2));
 

0.1180346e-2 

> taylor(sqrt(x),x=1,45);
 

series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1... 

> T45:=x->1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1)^12+52003/8388608*(x-1)^13-185725/33554432*(x-1)^14+334305/67108864*(x-1)^15-9694845/2147483648*(x-1)^16+17678835/4294967296*(x-1)^17-64822395/17179869184*(x-1)^18+119409675/34359738368*(x-1)^19-883631595/274877906944*(x-1)^20+1641030105/549755813888*(x-1)^21-6116566755/2199023255552*(x-1)^22+11435320455/4398046511104*(x-1)^23-171529806825/70368744177664*(x-1)^24+322476036831/140737488355328*(x-1)^25-1215486600363/562949953421312*(x-1)^26+2295919134019/1125899906842624*(x-1)^27-17383387729001/9007199254740992*(x-1)^28+32968493968795/18014398509481984*(x-1)^29-125280277081421/72057594037927936*(x-1)^30+238436656380769/144115188075855872*(x-1)^31-14544636039226909/9223372036854775808*(x-1)^32+27767032438524099/18446744073709551616*(x-1)^33-106168065206121555/73786976294838206464*(x-1)^34+203236010537432691/147573952589676412928*(x-1)^35-1558142747453650631/1180591620717411303424*(x-1)^36+2989949596465113373/2361183241434822606848*(x-1)^37-11487701081155435591/9444732965739290427392*(x-1)^38+22091732848375837675/18889465931478580854784*(x-1)^39-340212685864987900195/302231454903657293676544*(x-1)^40+655531760569123027205/604462909807314587353088*(x-1)^41-2528479647909474533505/2417851639229258349412352*(x-1)^42+4880553738988055494905/4835703278458516698824704*(x-1)^43-37713369801271337915175/38685626227668133590597632*(x-1)^44;
 

(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-...
(Typesetting:-mprintslash)([T45 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-... 

> plot({sqrt(x),T45(x)},x=1.9..2.1,thickness=2);
 

Plot 

> evalf(sqrt(2)-T45(2));
 

0.479080e-3 

> taylor(sqrt(x),x=1,100);
 

series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1...
series(1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10+4199/524288*(x-1)^11-29393/4194304*(x-1... 

> T100:=x->1+1/2*(x-1)-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*\
(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9-2431/262144*(x-1)^10\
+4199/524288*(x-1)^11-29393/4194304*(x-1)^12+52003/8388608*(x-1)^13-185725/33554\
432*(x-1)^14+334305/67108864*(x-1)^15-9694845/2147483648*(x-1)^16+17678835/42949\
67296*(x-1)^17-64822395/17179869184*(x-1)^18+119409675/34359738368*(x-1)^19-8836\
31595/274877906944*(x-1)^20+1641030105/549755813888*(x-1)^21-6116566755/21990232\
55552*(x-1)^22+11435320455/4398046511104*(x-1)^23-171529806825/70368744177664*(x\
-1)^24+322476036831/140737488355328*(x-1)^25-1215486600363/562949953421312*(x-1)\
^26+2295919134019/1125899906842624*(x-1)^27-17383387729001/9007199254740992*(x-1\
)^28+32968493968795/18014398509481984*(x-1)^29-125280277081421/72057594037927936\
*(x-1)^30+238436656380769/144115188075855872*(x-1)^31-14544636039226909/92233720\
36854775808*(x-1)^32+27767032438524099/18446744073709551616*(x-1)^33-10616806520\
6121555/73786976294838206464*(x-1)^34+203236010537432691/147573952589676412928*(\
x-1)^35-1558142747453650631/1180591620717411303424*(x-1)^36+2989949596465113373/\
2361183241434822606848*(x-1)^37-11487701081155435591/9444732965739290427392*(x-1\
)^38+22091732848375837675/18889465931478580854784*(x-1)^39-340212685864987900195\
/302231454903657293676544*(x-1)^40+655531760569123027205/60446290980731458735308\
8*(x-1)^41-2528479647909474533505/2417851639229258349412352*(x-1)^42+48805537389\
88055494905/4835703278458516698824704*(x-1)^43-37713369801271337915175/386856262\
27668133590597632*(x-1)^44+72912514949124586636005/77371252455336267181195264*(x\
-1)^45-282139731759656009156715/309485009821345068724781056*(x-1)^46+54627054447\
0823336877895/618970019642690137449562112*(x-1)^47-16934386878595523443214745/19\
807040628566084398385987584*(x-1)^48+32831974560542341369497975/3961408125713216\
8796771975168*(x-1)^49-127388061294904284513652143/15845632502852867518708790067\
2*(x-1)^50+247282707219520081702971807/316912650057057350374175801344*(x-1)^51-1\
921196417628579096307704039/2535301200456458802993406410752*(x-1)^52+37336458682\
21578243767802189/5070602400912917605986812821504*(x-1)^53-145197339319728042813\
19230735/20282409603651670423947251286016*(x-1)^54+28247482376747091965475594339\
/40564819207303340847894502572032*(x-1)^55-439853654152204717748119968993/649037\
107316853453566312041152512*(x-1)^56+856557115980609187193707308039/129807421463\
3706907132624082305024*(x-1)^57-3337619107096856488030652614083/5192296858534827\
628530496329220096*(x-1)^58+6505528768070144002093644925755/10384593717069655257\
060992658440192*(x-1)^59-50743124390947123216330430420889/8307674973655724205648\
7941267521536*(x-1)^60+98990685287257502667923298689931/166153499473114484112975\
882535043072*(x-1)^61-386382997411553478155442552951021/664613997892457936451903\
530140172288*(x-1)^62+754366804470175838303483079571041/132922799578491587290380\
7060280344576*(x-1)^63-94295850558771979787935384946380125/170141183460469231731\
687303715884105728*(x-1)^64+184239584937908329739504521356773475/340282366920938\
463463374607431768211456*(x-1)^65-720209286575459834436244947121932675/136112946\
7683753853853498429727072845824*(x-1)^66+1408170396140078183748478926462286275/2\
722258935367507707706996859454145691648*(x-1)^67-1101686251097825873167927630702\
8474975/21778071482940061661655974875633165533184*(x-1)^68+215547309997400714315\
46410165925277125/43556142965880123323311949751266331066368*(x-1)^69-84371375627\
553993889195948363764656175/174224571863520493293247799005065324265472*(x-1)^70+\
165177763552535283811242772148778693075/3484491437270409865864955980101306485309\
44*(x-1)^71-2587784962323052779709470096997532858175/557518629963265578538392956\
8162090376495104*(x-1)^72+5069222597427349965732249642063660256425/1115037259926\
5311570767859136324180752990208*(x-1)^73-198658723412693444603020594080873172211\
25/44601490397061246283071436545296723011960832*(x-1)^74+38937109788887915142192\
036439851141753405/89202980794122492566142873090593446023921664*(x-1)^75-3053489\
13607594702957190180501990532697755/71362384635297994052914298472474756819137331\
2*(x-1)^76+598801116295412988916048276049358057628065/14272476927059598810582859\
69449495136382746624*(x-1)^77-2349142840851235571901420159885943149156255/570899\
0770823839524233143877797980545530986496*(x-1)^78+460907772572077865373063449091\
5458077458475/11417981541647679048466287755595961091061972992*(x-1)^79-144725040\
587632449727141923014745383632196115/3653754093327257295509212081790707549139831\
35744*(x-1)^80+284089894486834067982908219251166864166903485/7307508186654514591\
01842416358141509827966271488*(x-1)^81-11155725124970801206158103243765332958749\
13685/2923003274661805836407369665432566039311865085952*(x-1)^82+219082312695209\
7104341892564739456954549529285/584600654932361167281473933086513207862373017190\
4*(x-1)^83-17213610283195048676972013008667161785746301525/467680523945888933825\
17914646921056628989841375232*(x-1)^84+33819681379924389753580307911146070802583\
910055/93536104789177786765035829293842113257979682750464*(x-1)^85-1329192128652\
84229496629582255434557340387925565/37414441915671114706014331717536845303191873\
1001856*(x-1)^86+261255004597282795907168489260681716151796957145/74828883831342\
2294120286634350736906063837462003712*(x-1)^87-410882870866635669926728624019072\
1535841897598735/11972621413014756705924586149611790497021399392059392*(x-1)^88+\
8079157573220364296312079685768272682835191907625/239452428260295134118491722992\
23580994042798784118784*(x-1)^89-31778019788000099565494180097355205885818421503\
325/95780971304118053647396689196894323976171195136475136*(x-1)^90+6250841255002\
2173870587453158533866522653818121925/191561942608236107294793378393788647952342\
390272950272*(x-1)^91-491914029198000585677231696595418688721753960002975/153249\
5540865888858358347027150309183618739122183602176*(x-1)^92+967959863905743087945\
520435236146452000870695489725/3064991081731777716716694054300618367237478244367\
204352*(x-1)^93-3810054783458775984466410223801853055748108056714875/12259964326\
927110866866776217202473468949912977468817408*(x-1)^94+7499792047439906411528618\
019483647593946275859007175/2451992865385422173373355243440494693789982595493763\
4816*(x-1)^95-472486898988714103926302935227469798418615379117452025/15692754338\
46670190958947355801916604025588861116008628224*(x-1)^96+93036080110148859639096\
7635344811664927376674344673575/313855086769334038191789471160383320805117772223\
2017256448*(x-1)^97-3664482339032393859254219461664258190428238737724938775/1255\
4203470773361527671578846415332832204710888928069025792*(x-1)^98+721791975870016\
9722773462576005357041752591453094576375/251084069415467230553431576928306656644\
09421777856138051584*(x-1)^99;
 

(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9...
(Typesetting:-mprintslash)([T100 := proc (x) options operator, arrow; 1/2+1/2*x-1/8*(x-1)^2+1/16*(x-1)^3-5/128*(x-1)^4+7/256*(x-1)^5-21/1024*(x-1)^6+33/2048*(x-1)^7-429/32768*(x-1)^8+715/65536*(x-1)^9... 

> evalf(sqrt(2)-T100(2));
 

-0.142644e-3 

> plot({sqrt(x),T100(x)},x=1.9..2.1,y=1.2..2,thickness=2);
 

Plot 

> taylor(sqrt(49/25+x),x=0,3);
 

series(7/5+5/14*x-125/2744*x^2+O(x^3),x,3) 

> TT3:=x->7/5+5/14*x-125/2744*x^2;
 

(Typesetting:-mprintslash)([TT3 := proc (x) options operator, arrow; 7/5+5/14*x-125/2744*x^2 end proc], [proc (x) options operator, arrow; 7/5+5/14*x-125/2744*x^2 end proc]) 

> evalf[15](sqrt(2)-TT3(1/25));
 

0.73438476e-6 

>
 

>