lim _{x rightarrow infty}left(frac{x+5}{x+2}r | vedclass

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Question

(C) We know that $\lim _{x \rightarrow \infty} (1 + \frac{a}{x+b})^{x+c} = e^a$. Given expression: $\lim _{x \rightarrow \infty} (\frac{x+5}{x+2})^{x+

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$e^3$

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(C) We know that $\lim _{x \rightarrow \infty} (1 + \frac{a}{x+b})^{x+c} = e^a$. Given expression: $\lim _{x \rightarrow \infty} (\frac{x+5}{x+2})^{x+3} = \lim _{x \rightarrow \infty} (1 + \frac{3}{x+2})^{x+3}$. Let $t = x+2$,then as $x \rightarrow \infty$,$t \rightarrow \infty$. $= \lim _{t \rightarrow \infty} (1 + \frac{3}{t})^{t+1} = \lim _{t \rightarrow \infty} (1 + \frac{3}{t})^t \cdot (1 + \frac{3}{t})^1$. $= e^3 \cdot 1 = e^3$.

$\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}$ equals

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