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Consider the function given by:

$$ f(x) = \left\{ \begin{array}{lll} -x-1 & x \lt -1 \\\ -x^2+1 & -1< x < 1 \\\ x + 1 & x \ge 1 \end{array} \right.$$

For which values of $a$ does $\lim \limits_{x \to a} f(x)$ not exist?

A

$a = 1$ or $-1$ only.

B

$a = -1$ only.

C

$a = 1$ only.

D

$\lim \limits_{x \to a} f(x)$ exists for all values of $a$.

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