Evaluate _ x - 2 1 x + 1 2 x + 2 - Vidyadip

Question

Evaluate $\mathop {\lim }\limits_{x \to - 2} \frac{{\frac{1}{x} + \frac{1}{2}}}{{x + 2}}$

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Answer

Here $\mathop {\lim }\limits_{x \to - 2} \frac{{\frac{1}{x} + \frac{1}{2}}}{{x + 2}}$
$ = \mathop {\lim }\limits_{x \to - 2} \frac{{\frac{{x + 2}}{{2x}}}}{{x + 2}}$
$ = \mathop {\lim }\limits_{x \to - 2} \frac{{x + 2}}{{2x}} \times \frac{1}{{x + 2}}$
$ = \mathop {\lim }\limits_{x \to - 2} \frac{1}{{2x}} = \frac{1}{{2 \times - 2}} = \frac{{ - 1}}{4}$

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