Chapter 3: Q. 39 (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.
$\lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln (x^{2} - 4)}$ .

Short Answer

Expert verified

The exact value of $\lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln (x^{2} - 4)}$ is, $1$ .

Step by step solution

Step 1. Given information

$\lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln (x^{2} - 4)}$ .

Step 2. The limit is given below:

$\lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln (x^{2} - 4)} = \lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln [(x - 2) (x + 2)]} = \lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln (x - 2) + \ln (x + 2)} = \lim_{x \to 2^{+}} \frac{1}{\frac{\ln (x - 2)}{\ln (x + 2)} + 1} = \frac{1}{0 + 1} = 1$

The exact value is, $1 .$

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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.
$\lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln (x^{2} - 4)}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit 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→2+ln(x-2)lnx2-4.

Short Answer

Step by step solution

Step 1. Given information

Step 2. The limit is given below:

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 $21 - 48$ . Some of these limits are made easier by L’Hopital’s rule, and some are not.
$\lim_{x \to 2^{+}} \frac{\ln (x - 2)}{\ln (x^{2} - 4)}$ .