I am asked to find the derivative function of [itex]f(x)=e^{x-2}[/itex] using the definition. That is to say, I have to evaluate this limit, if it exists:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\lim_{x\rightarrow x_0}\frac{e^{x-2} - e^{x_0-2}}{x-x_0} = \lim_{x\rightarrow x_0}\frac{e^{x} - e^{x_0}}{e^2 (x-x_0)}[/tex]

How can this undeterminate form be simplified? Thanks.

(The answer is [itex]f'(x_0)=e^{x_0-2}[/itex].)

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# Derivative of e^(x-2)

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