Taylor polynomial
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1) Calculate the Taylor polynomial of degree n at 0 of the function .
2)
• suppose that f''(x)=0 for all . Show that f has the form f(x)=ax+b for some real numbers a,b.
• 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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