▶️ Answer/Explanation
Solution
1. $\displaystyle \lim_{x \to -2} f(x) = \text{DNE}$
$\displaystyle \lim_{x \to -2^-} f(x) = -1$, because as $f(x)$ approaches 2 from the left side, the limit is -1.
$\displaystyle \lim_{x \to -2^+} f(x) = -3$, because as $f(x)$ approaches 2 from the right side, the limit is -3.
Different limits from each side mean that the limit at the point, which is -2, doesn’t exist.
2. $\displaystyle \lim_{x \to -3} f(x) = 4$
3. $\displaystyle \lim_{x \to 0} f(x) = 0$
4. $\displaystyle \lim_{x \to 2} f(x) = 1$