Chapter 3: Q. 36 (page 311)

Calculate each of the limits in Exercises $21 - 48$ . Some of these limits are made easier by L’Hopital’s rule, and some are not.
$\lim_{x \to \infty} \frac{\ln x}{\ln (2 x + 1)}$ .

Short Answer

Expert verified

The value of the limit $\lim_{x \to \infty} \frac{\ln x}{\ln (2 x + 1)}$ is, $0 .$

Step by step solution

Step 1. Given information

$\lim_{x \to \infty} \frac{\ln x}{\ln (2 x + 1)}$ .

Step 2. The limit using L'Hopital's rule is given below:

$\lim_{x \to \infty} \frac{\ln x}{\ln (2 x + 1)} = \lim_{x \to \infty} \frac{\frac{1}{x}}{\frac{1}{2 x + 1}}$ [L'Hopital's rule]

$= \lim_{x \to \infty} (\frac{1}{x} + \frac{1}{2 x + 1}) = \lim_{x \to \infty} (\frac{1}{2 x^{2} + x}) = \frac{1}{\infty} = 0$

The value of the limit is, $0$ .

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Calculate each of the limits in Exercises $21 - 48$ . Some of these limits are made easier by L’Hopital’s rule, and some are not.
$\lim_{x \to \infty} \frac{\ln x}{\ln (2 x + 1)}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit using L'Hopital's rule is given below:

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Calculate each of the limits in Exercises 21-48. Some of these limits are made easier by L’Hopital’s rule, and some are not.limx→∞lnxln(2x+1).

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit using L'Hopital's rule is given below:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Calculate each of the limits in Exercises $21 - 48$ . Some of these limits are made easier by L’Hopital’s rule, and some are not.
$\lim_{x \to \infty} \frac{\ln x}{\ln (2 x + 1)}$ .