Chapter 3: Q. 41 (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.
$\lim_{x \to 0} \frac{\cos x - 1}{\sin x}$ .

Short Answer

Expert verified

The exact value of $\lim_{x \to 0} \frac{\cos x - 1}{\sin x}$ is, $0$ .

Step by step solution

Step 1. Given information

$\lim_{x \to 0} \frac{\cos x - 1}{\sin x}$ .

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

$\lim_{x \to 0} \frac{\cos x - 1}{\sin x} = \lim_{x \to 0} \frac{- \sin x}{\cos x}$ [L'Hopital's rule]

$= - \frac{0}{1} = 0$

The exact value 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.
$\lim_{x \to 0} \frac{\cos x - 1}{\sin x}$ .

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→0cosx-1sinx.

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

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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.
$\lim_{x \to 0} \frac{\cos x - 1}{\sin x}$ .