Find mathop {lim }limits_{x to 1} f(x),where | vedclass

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(D) The given function is $f(x) = \begin{cases} x^{2}-1, & x \leq 1 \ -x-1, & x > 1 \end{cases}$To find the limit as $x 	o 1$,we evaluate the left-h

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Does not exist

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(D) The given function is $f(x) = \begin{cases} x^{2}-1, & x \leq 1 \ -x-1, & x > 1 \end{cases}$To find the limit as $x 	o 1$,we evaluate the left-hand limit and the right-hand limit.Left-hand limit:$\mathop {\lim }\limits_{x 	o 1^-} f(x) = \mathop {\lim }\limits_{x 	o 1} (x^{2}-1) = 1^{2}-1 = 0$Right-hand limit:$\mathop {\lim }\limits_{x 	o 1^+} f(x) = \mathop {\lim }\limits_{x 	o 1} (-x-1) = -1-1 = -2$Since $\mathop {\lim }\limits_{x 	o 1^-} f(x) 
eq \mathop {\lim }\limits_{x 	o 1^+} f(x)$,Therefore,$\mathop {\lim }\limits_{x 	o 1} f(x)$ does not exist.

Find $\mathop {\lim }\limits_{x \to 1} f(x)$,where $f(x) = \begin{cases} x^{2}-1, & x \leq 1 \\ -x-1, & x > 1 \end{cases}$

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