review the graph of function f(x). for which value of c does the limit not exist? lim f(x) as x→c -2 2 4 -4

Answer

Explanation:

Step1: Recall limit - existence condition

The limit $\lim_{x\rightarrow c}f(x)$ exists if and only if $\lim_{x\rightarrow c^{-}}f(x)=\lim_{x\rightarrow c^{+}}f(x)$.

Step2: Analyze $x = - 2$

As $x$ approaches $-2$ from the left and from the right, the function approaches the same value. So, $\lim_{x\rightarrow - 2}f(x)$ exists.

Step3: Analyze $x = 2$

As $x$ approaches $2$ from the left, the function approaches a higher - value, and as $x$ approaches $2$ from the right, the function approaches a lower - value. The left - hand limit $\lim_{x\rightarrow 2^{-}}f(x)\neq\lim_{x\rightarrow 2^{+}}f(x)$. So, $\lim_{x\rightarrow 2}f(x)$ does not exist.

Step4: Analyze $x = 4$

As $x$ approaches $4$ from the left and from the right, the function approaches the same value. So, $\lim_{x\rightarrow 4}f(x)$ exists.

Step5: Analyze $x=-4$

As $x$ approaches $-4$ from the left and from the right, the function approaches the same value. So, $\lim_{x\rightarrow - 4}f(x)$ exists.