i. Expand f(x)= x^5+x^3+x in powers of (x-1), using Taylor's theorem(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Homework Help: F(x)=sinx with taylor's theorem

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