Chapter 1: Q. 43 (page 149)

Calculate each limit in Exercises 35–80.
$\underset{x \to - 4}{l i m} \frac{x^{2} + 8 x + 16}{{(x + 4)}^{2} (x + 1)}$

Short Answer

Expert verified

The limit is $- \frac{1}{3}$

Step by step solution

Step 1. Given Information:

Given expression is $\underset{x \to - 4}{l i m} \frac{x^{2} + 8 x + 16}{{(x + 4)}^{2} (x + 1)}$

We want to find the limit of given expression.

Step 2. Calculation:

The limit is calculated as below:

$\underset{x \to - 4}{l i m} \frac{x^{2} + 8 x + 16}{{(x + 4)}^{2} (x + 1)}$

Obtain factor of numerator of expression we get

$\underset{x \to - 4}{l i m} \frac{{(x + 4)}^{2}}{{(x + 4)}^{2} (x + 1)} = \underset{x \to - 4}{l i m} \frac{1}{(x + 1)}$

Now put limit we get

$\underset{x \to - 4}{l i m} \frac{1}{(x + 1)} = \frac{1}{(- 4 + 1)} = - \frac{1}{3}$

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Calculate each limit in Exercises 35–80.
$\underset{x \to - 4}{l i m} \frac{x^{2} + 8 x + 16}{{(x + 4)}^{2} (x + 1)}$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Calculation:

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Calculate each limit in Exercises 35–80.limx→-4x2+8x+16(x+4)2(x+1)

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Calculation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Calculate each limit in Exercises 35–80.
$\underset{x \to - 4}{l i m} \frac{x^{2} + 8 x + 16}{{(x + 4)}^{2} (x + 1)}$