$\lim_{x \to 5} \frac{e^{x} - e^{5}}{x - 5}$

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Solution

$\lim_{x \to 5} [\frac{e^{x} - e^{5}}{x - 5}] = \lim_{x \to 5} e^{5} [\frac{e^{x - 5} - 1}{x - 5}] = e^{5} \times 1$

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