Chapter 12.2, Problem 38E

To determine

To evaluate:The one sidedlimits of the given function and sketch the graph.

Answer to Problem 38E

Limit of the function is $\frac{1}{2}$ .

Explanation of Solution

Given:

  ${\underrightarrow{\lim }}_{h\to 1}\frac{1}{x^2+1}$

Explanation:Let

  ${\underrightarrow{\lim }}_{h\to 1}\frac{1}{x^2+1}$ be a given function.

It has to find one sided limits.

Graph of the function ${\underrightarrow{\lim }}_{h\to 1}\frac{1}{x^2+1}$ is

  

From graph of function,

  $f\left(x\right)=\frac{1}{2}$ at $x=-1$ .

So, the limit from the left is ${\underrightarrow{\lim }}_{h\to 1^{-}}\frac{1}{x^2+1}=\frac{1}{2}$

Hence, limit of the function ${\underrightarrow{\lim }}_{h\to 1^{-}}\frac{1}{x^2+1}=\frac{1}{2}$ .