Chapter 1: Q. 26 (page 135)

Calculate the limits in Exercises 25–28, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
$lim_{x \to - 1} \frac{x - 1}{(x + 4) (x + 2)}$

Short Answer

Expert verified

$lim_{x \to - 1} \frac{x - 1}{(x + 4) (x + 2)} = \frac{2}{3}$

Step by step solution

Step 1. Given information.

We have to calculate the limit of the given function.

Function is:

$lim_{x \to - 1} \frac{x - 1}{(x + 4) (x + 2)}$

Step 2. Calculate the limit

The limit of the function can be calculated as:

$\begin{aligned} lim_{x \to - 1} \frac{x - 1}{(x + 4) (x + 2)} \\ = \frac{lim_{x \to - 1} (x - 1)}{lim_{x \to - 1} (x + 4) (x + 2)} \\ = \frac{lim_{x \to - 1} (x - 1)}{lim_{x \to - 1} (x + 4) lim_{x \to - 1} (x + 2)} \\ = \frac{(- 1) - 1}{(- 1 + 4) (- 1 + 2)} \\ = \frac{- 1 - 1}{3 (1)} \\ = \frac{- 2}{3} \\ = \frac{2}{3} \end{aligned}$

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Calculate the limits in Exercises 25–28, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
$lim_{x \to - 1} \frac{x - 1}{(x + 4) (x + 2)}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the limit

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Calculate the limits in Exercises 25–28, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.limx→−1 x−1(x+4)(x+2)

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Probability and Statistics

Pure Maths

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Calculate the limits in Exercises 25–28, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.
$lim_{x \to - 1} \frac{x - 1}{(x + 4) (x + 2)}$