f(x)=sin^2x, k=4
f(x)=chx, k=5
sin^2x=(1-cos2x)/2
cosx=1-(x^2/2!)+(x^4/4!)+o(x^4)
cos2x=1-((2x)^2/2!)+((2x)^4/4!)+o(x^4)
-cos2x=-1+((2x)^2/2!)-((2x)^4/4!)+o(x^4)
1-cos2x=((2x)^2/2!)-((2x)^4/4!)+o(x^4)
(1-cos2x)/2=(1/2)*((2x)^2/2!)-(1/2)*((2x)^4/4!)+o(x^4)
sin^2x=(1/2)*((2x)^2/2!)-(1/2)*((2x)^4/4!)+o(x^4)
2)
chx=(e^x+e^(-x))/2
e^x=1+x+(x^2/2!)+(x^3/3!)+(x^4/4!)+(x^5/5!)+o(x^5)
e^(-x)=1-x+(x^2/2!)-(x^3/3!)+(x^4/4!)-(x^5/5!)+o(x^5)
e^x+e^(-x)=2+2*((x^2/2!))+2*(x^4/4!)+o(x^5)
(e^x+e^(-x))/2=1+(x^2/2!))+(x^4/4!)+o(x^5)
chx=1+(x^2/2!))+(x^4/4!)+o(x^5)