Chapter 2.2, Problem 58E

To determine

Tocheck:Whether the limit $\underset{x\to c}{\lim }\left(f\left(x\right)+g\left(x\right)\right)$ can be determined or not.

Answer to Problem 58E

The value of $\underset{x\to c}{\lim }\left(f\left(x\right)+g\left(x\right)\right)$ can’t be determined.

Explanation of Solution

Given information:

Let $\text{L}$ be a real number, $\underset{x\to c}{\lim }f\left(x\right)=\text{L}$ and $\underset{x\to c}{\lim }g\left(x\right)=\infty$ or $-\infty$ .

Calculation:

If the value $\underset{x\to c}{\lim }g\left(x\right)=\infty$ or $-\infty$ and $\underset{x\to c}{\lim }f\left(x\right)=\text{L}$ .

Then the value of $\underset{x\to c}{\lim }\left(f\left(x\right)+g\left(x\right)\right)$ can’t be determined as it can give a finite value as we need functions for this.