Question

In Problems 7–16, use a table to find the indicated limit.

$9.\underset{x\to 0}{\lim }\frac{x+1}{x^2+1}$

Short answer

$\underset{x\to 0}{\lim }\frac{x+1}{x^2+1}=1$.

Step-by-step solution

Step 1. Given information.

A limit function is given as $\underset{x\to 0}{\lim }\frac{x+1}{x^2+1}$.

Step 2. Make the table to find limit.

Choose values of x close to 0, arbitrarily starting with -0.01 then we select additional numbers that get closer to 0, but remain less than 0. Next choose values of x greater than 0 , staring with 0.01, which get closer to 0.

Finally evaluate the given function at each choice to obtain the below table :

As x gets closer to 0, the value of $f\left(x\right)=\frac{x+1}{x^2+1}$gets closer to 1.

So,role="math" localid="1647485079023" $\underset{x\to c}{\lim }\frac{x+1}{x^2+1}=1$.