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(a) Show that the function defined by

$ f(x) = \left\{\begin{array} (e^{-1/x^2} \text{ if } x \not= 0 \\0 \text { if } x = 0 \end{array}\right. $

is not equal to its Maclaurin series.

(b) Graph the function in part (a) and comment on its behavior near the origin.

a. see work for answer

b. see work for graph

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