Chapter 1: Q. 31 (page 135)

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to - 1} (x^{2} - \frac{3 x}{x + 2})$ .

Short Answer

Expert verified

The value of $\lim_{x \to - 1} (x^{2} - \frac{3 x}{x + 2})$ is, $4$ .

Step by step solution

Step 1. Given information

$\lim_{x \to - 1} (x^{2} - \frac{3 x}{x + 2})$ .

Step 2. The limit is calculated as below:

$\lim_{x \to - 1} (x^{2} - \frac{3 x}{x + 2}) = \lim_{x \to - 1} (x^{2}) - \lim_{x \to - 1} (\frac{3 x}{x + 2})$ [Sum rule]

$= \lim_{x \to - 1} (x^{2}) - \frac{\lim_{x \to - 1} (3 x)}{\lim_{x \to - 1} (x + 2)}$ [Quotient rule]

$= {(- 1)}^{2} - \frac{(- 3)}{(- 1 + 2)} = 1 - \frac{(- 3)}{1} = 1 + 3 = 4$

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Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to - 1} (x^{2} - \frac{3 x}{x + 2})$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below:

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Calculate each of the limits in Exercises 29-70.limx→-1x2-3xx+2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below:

One App. One Place for Learning.

Most popular questions from this chapter

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to - 1} (x^{2} - \frac{3 x}{x + 2})$ .