(adsbygoogle = window.adsbygoogle || []).push({}); CLUELESS about a Maclaurin series!!

I'm supposed to obtain a Maclaurin series for the function defined by

[tex] f(x) = \left\{ \begin{array}{lc} e^{-1/x^2} & \mbox{ if } x \neq 0 \\

0 & \mbox{ if } x = 0 \end{array} \right. [/tex]

I get immediately stuck as I find:

[tex] f(0) = 0 [/tex]

[tex] f^{\prime}(0) = \mbox{ undefined } [/tex]

[tex] f^{\prime \prime}(0) = \mbox{ undefined } [/tex]

[tex] f^{\prime \prime \prime}(0) = \mbox{ undefined } [/tex]

[tex] f^{(4)}(0) = \mbox{ undefined } [/tex]

So,

[tex] f^{(n)}(0) = \mbox{ undefined } \qquad n > 0 [/tex]

Thus, we may write

[tex] f(x) = f(0) + \frac{f^{\prime}(0)}{1!}x + \frac{f^{\prime \prime}(0)}{2!}x^2 + \frac{f^{\prime \prime \prime}(0)}{3!}x^3 + \cdots [/tex]

Question

How do I handle the undefined results? (I'm supposed to show that the Maclaurin series is not equal to the given function)

Thank you very much.

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# Homework Help: CLUELESS about a Maclaurin series

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