the function f(x) has values as given in the table. x 4.9 4.99 4.999 5.001 5.01 5.1 f(x) 10 100 1000 -1000…

Explanation:

Step1: Recall limit definition

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

Step2: Find left - hand limit

As $x$ approaches $5$ from the left ($x = 4.9,4.99,4.999$), $f(x)$ values are $10,100,1000$. So, $\lim_{x\rightarrow 5^{-}}f(x)=\infty$.

Step3: Find right - hand limit

As $x$ approaches $5$ from the right ($x = 5.001,5.01,5.1$), $f(x)$ values are $- 1000,-100,-10$. So, $\lim_{x\rightarrow 5^{+}}f(x)=-\infty$.

Step4: Compare left - hand and right - hand limits

Since $\lim_{x\rightarrow 5^{-}}f(x)\neq\lim_{x\rightarrow 5^{+}}f(x)$, the limit does not exist.

Answer:

DNE