i. Expand f(x)= x^5+x^3+x in powers of (x-1), using Taylor's theorem ii. Consider f(x)= sin x. Find the Taylor polynomial T of degree 7 expanded at [tex]\pi\[/tex]/3. Give an estimate for the remainder term, in the form |sin (x)- T(x)|[tex]\leq[/tex] C|x-[tex]\pi[/tex]/3|^8 with a suitable (good) constant C. f(x)= f(1)+f'(1)(x-1)+f''(1)(x-1)^2.... + f^(n)(1)/n!(x-1)^(n) is that right for i? and for ii... i'm not sure what to do.