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Evaluate \(\lim\limits_{\text x \to0}\left(\cfrac{3^{2+\text x}-9}{\text x}\right) \)

lim(x→0)(32 + x - 9)/x

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To evaluate \(\lim\limits_{\text x \to0}\left(\cfrac{3^{2+\text x}-9}{\text x}\right) \)

lim(x→0)(32 + x - 9)/x

Formula used: L'Hospital's rule

Let f(x) and g(x) be two functions which are differentiable on an open interval I except at a point a where

This represents an indeterminate form. Thus applying L'Hospital's rule, we get

Thus, the value of \(\lim\limits_{\text x \to0}\cfrac{3^{2+\text x}-9}{\text x}\) is 2 In3

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