Find mathop {lim }limits_{x to 0} f(x) where | vedclass

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(D) To find $\mathop {\lim }\limits_{x 	o 0} f(x)$,we evaluate the left-hand limit $(LHL)$ and the right-hand limit $(RHL)$.$LHL$: $\mathop {\lim }\l

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Does not exist

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(D) To find $\mathop {\lim }\limits_{x 	o 0} f(x)$,we evaluate the left-hand limit $(LHL)$ and the right-hand limit $(RHL)$.$LHL$: $\mathop {\lim }\limits_{x 	o 0^-} f(x) = \mathop {\lim }\limits_{x 	o 0^-} \frac{x}{|x|}$.Since $x $RHL$: $\mathop {\lim }\limits_{x 	o 0^+} f(x) = \mathop {\lim }\limits_{x 	o 0^+} \frac{x}{|x|}$.Since $x > 0$,$|x| = x$,so $\mathop {\lim }\limits_{x 	o 0^+} \frac{x}{x} = \mathop {\lim }\limits_{x 	o 0^+} (1) = 1$.Since $\mathop {\lim }\limits_{x 	o 0^-} f(x) 
eq \mathop {\lim }\limits_{x 	o 0^+} f(x)$,the limit $\mathop {\lim }\limits_{x 	o 0} f(x)$ does not exist.

Find $\mathop {\lim }\limits_{x \to 0} f(x)$ where $f(x) = \begin{cases} \frac{x}{|x|}, & x \neq 0 \\ 0, & x=0 \end{cases}$

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