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 $\displaystyle f(x) = e^{x}$: $\displaystyle e^{x} \approx P_{3}(x) = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!}$ Note that $\displaystyle \sqrt{e} = e^{\frac{1}{2}}$ So simply plug 1/2 it in.
Originally Posted by matty888 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 $\displaystyle 0<y<1/2$). $\displaystyle \frac{f^{(4)}(y)}{4!}(1/2)^4 = \frac{e^y}{384}\leq \frac{\sqrt{3}}{384} $.
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