mathop {lim }limits_{x to 0} frac{|x|}{x} = | vedclass

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(D) The limit exists if and only if the left-hand limit and the right-hand limit are equal.For the left-hand limit: $\mathop {\lim }\limits_{x 	o 0^-

Vedclass · Accepted Answer

Does not exist

Vedclass · Answer

(D) The limit exists if and only if the left-hand limit and the right-hand limit are equal.For the left-hand limit: $\mathop {\lim }\limits_{x 	o 0^-} \frac{|x|}{x} = \mathop {\lim }\limits_{x 	o 0^-} \frac{-x}{x} = -1$.For the right-hand limit: $\mathop {\lim }\limits_{x 	o 0^+} \frac{|x|}{x} = \mathop {\lim }\limits_{x 	o 0^+} \frac{x}{x} = 1$.Since the left-hand limit $(-1)$ is not equal to the right-hand limit $(1)$,the limit does not exist.

$\mathop {\lim }\limits_{x \to 0} \frac{|x|}{x} = $

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