Chapter 1: Q. 37 (page 135)

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

Short Answer

Expert verified

The value of $\lim_{x \to - 3} \frac{x + 3}{3 x^{2} + 8 x - 3}$ is, $- \frac{1}{10}$ .

Step by step solution

Step 1. Given information

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

Step 2. The limit is calculated as below:

$\lim_{x \to - 3} \frac{x + 3}{3 x^{2} + 8 x - 3} = \lim_{x \to - 3} \frac{x + 3}{3 x^{2} + 9 x - x - 3} = \lim_{x \to - 3} \frac{x + 3}{3 x (x + 3) - 1 (x + 3)} = \lim_{x \to - 3} \frac{x + 3}{(3 x - 1) (x + 3)} = \lim_{x \to - 3} \frac{1}{(3 x - 1)} = \frac{1}{3 (- 3) - 1} = \frac{1}{- 9 - 1} \lim_{x \to - 3} \frac{x + 3}{3 x^{2} + 8 x - 3} = - \frac{1}{10}$

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

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→-3x+33x2+8x-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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Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to - 3} \frac{x + 3}{3 x^{2} + 8 x - 3}$ .