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

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(C) We know that $\lim _{x \rightarrow \infty} (1 + \frac{a}{x})^x = e^a$.Given expression: $\lim _{x \rightarrow \infty} (\frac{x+5}{x+2})^{x+3}$$= \

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$e^3$

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(C) We know that $\lim _{x \rightarrow \infty} (1 + \frac{a}{x})^x = e^a$.Given expression: $\lim _{x \rightarrow \infty} (\frac{x+5}{x+2})^{x+3}$$= \lim _{x \rightarrow \infty} (1 + \frac{3}{x+2})^{x+3}$$= \lim _{x \rightarrow \infty} [(1 + \frac{3}{x+2})^{\frac{x+2}{3}}]^{\frac{3(x+3)}{x+2}}$$= e^{\lim _{x \rightarrow \infty} \frac{3x+9}{x+2}}$$= e^{\lim _{x \rightarrow \infty} \frac{3 + 9/x}{1 + 2/x}}$$= e^3$

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

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