Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
**Limits in Trigonometry** **Objective**: Find the following limits. 1. \(\lim_{\theta \to 0} \frac{\cos(\theta) - 1}{\sin(\theta)}\) 2. \(\lim_{x \to 0} \csc(x) \cdot \sin(\sin(x))\) ### Explanation: 1. **Limit Problem 1**: - This limit involves the difference quotient of the cosine function as \(\theta\) approaches 0. It's often solved using trigonometric identities or L'Hôpital's Rule. 2. **Limit Problem 2**: - In this problem, explore the limit as \(x\) approaches 0 of the product of the cosecant function and the sine of sine function. This can be tackled by understanding the behavior of trigonometric functions close to zero. These exercises are designed to enhance skills in using trigonometric identities and calculus techniques to evaluate limits effectively.
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Transcribed Image Text:**Limits in Trigonometry** **Objective**: Find the following limits. 1. \(\lim_{\theta \to 0} \frac{\cos(\theta) - 1}{\sin(\theta)}\) 2. \(\lim_{x \to 0} \csc(x) \cdot \sin(\sin(x))\) ### Explanation: 1. **Limit Problem 1**: - This limit involves the difference quotient of the cosine function as \(\theta\) approaches 0. It's often solved using trigonometric identities or L'Hôpital's Rule. 2. **Limit Problem 2**: - In this problem, explore the limit as \(x\) approaches 0 of the product of the cosecant function and the sine of sine function. This can be tackled by understanding the behavior of trigonometric functions close to zero. These exercises are designed to enhance skills in using trigonometric identities and calculus techniques to evaluate limits effectively.
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