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    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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    https://brainmass.com/math/basic-algebra/taylor-polynomial-real-analysis-28201

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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
    ...

    Solution Summary

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

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