Given, lim_x → 03^2 + x 9x Now, [ =lim #160; #160;_ x→ 0 9× 3^ x 9 x #160;; =9lim # ...

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Existence of Limit

lim x→ 0 32+x...

Question

$lim x \to 0 \frac{3^{2 + x} - 9}{x}$

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Solution

Given,
$lim x \to 0 \frac{3^{2 + x} - 9}{x}$

Now,
$\begin{matrix} = {lim}_{x \to 0} \frac{9 \times 3^{x} - 9}{x} = 9 {lim}_{x \to 0} \frac{(3^{x} - 1)}{x} = 9 ln 3 \end{matrix}$

Hence, this is the answer.

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