Question

7.
Limx->2(1/(x-2)
(a) 2
(610
(c) 1
(d) does not exist​

Answer 1

$\\ \lim_{x \to2} (\frac{1}{x - 2} )$

Considering the Left Hand Limit First

$\\ \lim_{x \to2 ^{ - } } (\frac{1}{x - 2} ) = \frac{1}{2 ^{ - } - 2 } \to - \infty$

Now, Considering the Right hand Limit

$\\ \lim_{x \to2 ^{ + } } (\frac{1}{x - 2} ) = \frac{1}{ {2}^{ + } - 2 } \to + \infty$

Therefore, the Limit Does not exists.(D)