Chapter 14: Q. 9 (page 876)

In Problems 7–16, use a table to find the indicated limit.
$9 . \lim_{x \to 0} \frac{x + 1}{x^{2} + 1}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

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

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 $f (x) = \frac{x + 1}{x^{2} + 1}$ gets closer to 1.

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

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In Problems 7–16, use a table to find the indicated limit.
$9 . \lim_{x \to 0} \frac{x + 1}{x^{2} + 1}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Make the table to find limit.

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In Problems 7–16, use a table to find the indicated limit.9.limx→0x+1x2+1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Make the table to find limit.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Pure Maths

Geometry

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 7–16, use a table to find the indicated limit.
$9 . \lim_{x \to 0} \frac{x + 1}{x^{2} + 1}$