The value of lim_{x rightarrow 0} frac{|x|}{x | vedclass

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(D) We are given the limit $\lim_{x \rightarrow 0} \frac{|x|}{x}$.To evaluate this,we check the left-hand limit and the right-hand limit.For the right

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Does not exist

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(D) We are given the limit $\lim_{x ightarrow 0} \frac{|x|}{x}$.To evaluate this,we check the left-hand limit and the right-hand limit.For the right-hand limit $(x ightarrow 0^{+})$,$|x| = x$,so $\lim_{x ightarrow 0^{+}} \frac{x}{x} = 1$.For the left-hand limit $(x ightarrow 0^{-})$,$|x| = -x$,so $\lim_{x ightarrow 0^{-}} \frac{-x}{x} = -1$.Since the left-hand limit $
eq$ the right-hand limit,the limit does not exist.

The value of $\lim_{x \rightarrow 0} \frac{|x|}{x}$ is

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