Chapter 1: Q. 39 (page 135)

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to \frac{1}{2}} \frac{4 x - 2}{6 x^{2} + x - 2}$ .

Short Answer

Expert verified

The value of $\lim_{x \to \frac{1}{2}} \frac{4 x - 2}{6 x^{2} + x - 2}$ is, $\frac{4}{7}$ .

Step by step solution

Step 1. Given information

$\lim_{x \to \frac{1}{2}} \frac{4 x - 2}{6 x^{2} + x - 2}$ .

Step 2. The limit is calculated as below:

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

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

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

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Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to \frac{1}{2}} \frac{4 x - 2}{6 x^{2} + x - 2}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is calculated as below:

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

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Calculate each of the limits in Exercises 29-70.limx→124x-26x2+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 quotient rule in the obtained equation.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Calculate each of the limits in Exercises $29 - 70$ .
$\lim_{x \to \frac{1}{2}} \frac{4 x - 2}{6 x^{2} + x - 2}$ .