MCQ
$x\in R,$ માટે $\lim_{x \rightarrow \infty} {{\left( \frac{x-3}{x+2} \right)}^{x}}=........$
- A$e$
- B${{e}^{-1}}$
- ✓${{e}^{-5}}$
- D${{e}^{5}}$
$\lim_{x \rightarrow \infty} {{\left( \frac{x+2-5}{x+2} \right)}^{x}}$
$=\lim_{x \rightarrow \infty }\left[\left(1-\frac{5}{x+2}\right)^\frac{-(x+2)}{5}\right]^\frac{-5x}{x+2}$
$=e^{{\lim_{x \rightarrow \infty}}\frac{-5x}{x+2}}$
$=e^{-5}$
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