Chapter 1: Q. 42 (page 136)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

$\lim_{x \to 1^{+}} \frac{1 - \sqrt{x}}{1 - x}$ .

Step 2. The limit is calculated as below:

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

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

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→1+1-x1-x.

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 $29 - 70$ .
$\lim_{x \to 1^{+}} \frac{1 - \sqrt{x}}{1 - x}$ .