If f(x) = begin{cases} frac{x - |x|}{x}, & x | vedclass

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(B) To check the continuity of $f(x)$ at $x = 0$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 0$.$1$. Left-h

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$f(x)$ is discontinuous at $x = 0$

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(B) To check the continuity of $f(x)$ at $x = 0$,we evaluate the left-hand limit,right-hand limit,and the value of the function at $x = 0$.$1$. Left-hand limit $(LHL)$: $\lim_{x 	o 0^-} f(x) = \lim_{x 	o 0^-} \frac{x - (-x)}{x} = \lim_{x 	o 0^-} \frac{2x}{x} = 2$.$2$. Right-hand limit $(RHL)$: $\lim_{x 	o 0^+} f(x) = \lim_{x 	o 0^+} \frac{x - x}{x} = \lim_{x 	o 0^+} \frac{0}{x} = 0$.$3$. Value of the function: $f(0) = 2$.Since the left-hand limit $(2)$ is not equal to the right-hand limit $(0)$,the limit $\lim_{x 	o 0} f(x)$ does not exist.Therefore,$f(x)$ is discontinuous at $x = 0$.

If $f(x) = \begin{cases} \frac{x - |x|}{x}, & x \ne 0 \\ 2, & x = 0 \end{cases}$,then

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