# Taylor polynomial

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1) Calculate the Taylor polynomial of degree n at 0 of the function .

2)

â€¢ suppose that f''(x)=0 for all . Show that f has the form f(x)=ax+b for some real numbers a,b.

â€¢ let h:(-1,1) be defined by . Prove that there exists a positive integer m such that

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#### Solution Preview

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1) Calculate the Taylor polynomial of degree n at 0 of the function .

We know that

So,

So, the Taylor polynomial of degree n at 0 of the function is

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#### Solution Summary

This shows how to calculate the Taylor polynomial of degree n at 0 of a given function.

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