MCQ
$\mathop {\lim }\limits_{x \to \infty } {\left( {\frac{{x + 3}}{{x + 1}}} \right)^{x + 1}} = $
- ✓${e^2}$
- B${e^3}$
- C$e$
- D${e^{ - 1}}$
$ = \mathop {\lim }\limits_{x \to \infty } {\left( {1 + \frac{2}{{x + 1}}} \right)^{\frac{{x + 1}}{2}.2}}$
$ = {\left\{ {\mathop {\lim }\limits_{x \to \infty } {{\left( {1 + \frac{2}{{x + 1}}} \right)}^{\frac{{x + 1}}{2}}}} \right\}^2}$$ = {e^2}$.
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