Question

decide from the graph whether a limit exists. if a limit exists, find its value. lim f(x) x→ - 4 what is 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 \(-4\) from the left side (\(x\to - 4^{-}\)), the function values \(f(x)\) decrease without bound, \(\lim_{x\to - 4^{-}}f(x)=-\infty\).

Step2: Analyze right - hand limit

As \(x\) approaches \(-4\) from the right side (\(x\to - 4^{+}\)), the function values \(f(x)\) increase without bound, \(\lim_{x\to - 4^{+}}f(x)=\infty\).

Step3: Determine overall limit

Since the left - hand limit and the right - hand limit are not equal (one is \(-\infty\) and the other is \(\infty\)), the two - sided limit \(\lim_{x\to - 4}f(x)\) does not exist.

Answer:

B. The limit does not exist.