Chapter 1: Q. 38 (page 135)

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to - 3} \frac{3 x^{2} + 8 x - 3}{x + 3}$ .

Short Answer

Expert verified

The value of $\lim_{x \to - 3} \frac{3 x^{2} + 8 x - 3}{x + 3}$ is $- 10$ .

Step by step solution

Step 1. Given information

$\lim_{x \to - 3} \frac{3 x^{2} + 8 x - 3}{x + 3}$ .

Step 2. The limit is calculated as below:

$\lim_{x \to - 3} \frac{3 x^{2} + 8 x - 3}{x + 3} = \lim_{x \to - 3} \frac{3 x^{2} + 9 x - x - 3}{x + 3} = \lim_{x \to - 3} \frac{3 x (x + 3) - 1 (x + 3)}{x + 3} = \lim_{x \to - 3} \frac{(x + 3) (3 x - 1)}{(x + 3)} = \lim_{x \to - 3} (3 x - 1)$

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

$= 3 (- 3) - 1 = - 9 - 1 = - 10$

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Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to - 3} \frac{3 x^{2} + 8 x - 3}{x + 3}$ .

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→-33x2+8x-3x+3.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below:

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to - 3} \frac{3 x^{2} + 8 x - 3}{x + 3}$ .