Does the limit exist? Left- and right-hand limits with |x|, [x] or a piecewise function

1. A.
   1
2. B.
   $-1$
3. C.
   0
4. D.
   does not exist.

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1. A.
   0
2. B.
   1
3. C.
   $\sin 1$
4. D.
   $-\sin 1$

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1. A.
   1
2. B.
   $-1$
3. C.
   2
4. D.
   non-existent.

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1. A.
   0
2. B.
   1
3. C.
   -1
4. D.
   $\frac{1}{2}$

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1. A.
   $\infty$
2. B.
   $1$
3. C.
   $0$
4. D.
   does not exist

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1. A.
   $\lim_{x \to 2} f(x)$ exists and is equal to $5$
2. B.
   $\lim_{x \to 2} f(x)$ exists but is not equal to $5$
3. C.
   $\lim_{x \to 2} f(x)$ does not exist because $f(2)$ is defined
4. D.
   $\lim_{x \to 2} f(x)$ does not exist because left-hand and right-hand limits are not equal

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