Question

decide from the graph whether a limit exists. if a limit exists, find its value.
lim f(x)
x→ - 2
what is the value of the limit? select the correct choice below and fill in any answer boxes in your choice.
a. the limit is the real number
b. the limit does not exist.

Explanation:

Step1: Analyze left - hand limit

As $x$ approaches $- 2$ from the left side ($x\to - 2^{-}$), the function values seem to be approaching positive infinity.

Step2: Analyze right - hand limit

As $x$ approaches $- 2$ from the right side ($x\to - 2^{+}$), the function values seem to be approaching negative infinity.

Step3: Check limit existence

For $\lim_{x\to - 2}f(x)$ to exist, $\lim_{x\to - 2^{-}}f(x)=\lim_{x\to - 2^{+}}f(x)$. Since the left - hand limit and the right - hand limit are not equal (one is $\infty$ and the other is $-\infty$), the limit does not exist.

Answer:

B. The limit does not exist.