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Math Help - Taylor polynomial

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    Taylor polynomial

    Use the Taylor polynomial of order 3 for f(x) = e^x about x = 0 to

    approximate √e. Compare your approximation with the answer given by

    a calculator.
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    Given f(x) = e^{x}:

    e^{x} \approx P_{3}(x) = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!}

    Note that \sqrt{e} = e^{\frac{1}{2}}

    So simply plug 1/2 it in.
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    Quote Originally Posted by matty888 View Post
    Use the Taylor polynomial of order 3 for f(x) = e^x about x = 0 to

    approximate √e. Compare your approximation with the answer given by

    a calculator.
    Here is the accuracy. .
    (Note 0<y<1/2).

    \frac{f^{(4)}(y)}{4!}(1/2)^4 = \frac{e^y}{384}\leq \frac{\sqrt{3}}{384} .
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