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Carry out Taylor-series deployment of the following function. $$ \begin{align} f(x)&= \operatorname{sec}^2 x \tag{1}\\ g(x)&=\exp \left( -\frac{1}{(1-x)^2} \right) \tag{2} \end{align} $$ I could not be successful.

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I think if you understand Taylor Series at all, you would have been successful or at least you would be able to tell us what you've done so far. Visit Wikipedia's article on Taylor Series and then try again. –  user31280 Oct 26 '12 at 11:10

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