Chapter 1: Q. 40 (page 135)

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to \frac{- 2}{3}} \frac{6 x^{2} + x - 2}{3 x + 2}$ .

Short Answer

Expert verified

The value of $\lim_{x \to \frac{- 2}{3}} \frac{6 x^{2} + x - 2}{3 x + 2}$ is, $- \frac{7}{3}$ .

Step by step solution

Step 1. Given information

$\lim_{x \to \frac{- 2}{3}} \frac{6 x^{2} + x - 2}{3 x + 2}$ .

Step 2. The limit is calculated as below:

$\lim_{x \to - 2 / 3} \frac{6 x^{2} + x - 2}{3 x + 2} = \lim_{x \to - 2 / 3} \frac{6 x^{2} + 4 x - 3 x - 2}{3 x + 2} = \lim_{x \to - 2 / 3} \frac{2 x (3 x + 2) - 1 (3 x + 2)}{3 x + 2} = \lim_{x \to - 2 / 3} \frac{(2 x - 1) (3 x + 2)}{(3 x + 2)} = \lim_{x \to - 2 / 3} (2 x - 1)$

Step 3. Let us use the Sum rule in the obtained equation.

$\lim_{x \to - 2 / 3} (2 x - 1) = \lim_{x \to - 2 / 3} (2 x) - \lim_{x \to - 2 / 3} (1) = 2 (- \frac{2}{3}) - 1 = - \frac{4}{3} - 1 = - \frac{7}{3}$

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Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to \frac{- 2}{3}} \frac{6 x^{2} + x - 2}{3 x + 2}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below:

Step 3. Let us use the Sum rule in the obtained equation.

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Calculate each of the limits in Exercises 29-70.limx→-236x2+x-23x+2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below:

Step 3. Let us use the Sum rule in the obtained equation.

One App. One Place for Learning.

Most popular questions from this chapter

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Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to \frac{- 2}{3}} \frac{6 x^{2} + x - 2}{3 x + 2}$ .