Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Title: Calculating the Limit of \(\frac{\pi \sin \theta}{50 - 2 \sin \theta}\) as \(\theta \to 0\)
To find the limit of the expression \(\frac{\pi \sin \theta}{50 - 2 \sin \theta}\) as \(\theta\) approaches 0, follow these steps:
\[
\lim_{\theta \to 0} \frac{\pi \sin \theta}{50 - 2 \sin \theta}
\]
### Step-by-Step Calculation:
1. **Substitute \(\theta = 0\):**
Substitute \(\theta = 0\) directly into the equation:
\[
\frac{\pi \sin(0)}{50 - 2 \sin(0)} = \frac{\pi \cdot 0}{50 - 2 \cdot 0} = \frac{0}{50} = 0
\]
Therefore, the limit of \(\frac{\pi \sin \theta}{50 - 2 \sin \theta}\) as \(\theta\) approaches 0 is:
\[
\boxed{0}
\]
This shows that the value of the expression approaches 0 as \(\theta\) gets closer to 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ac30416-a057-4cd1-8bfb-7fbbdadcb376%2F76f6473e-d259-499e-8871-6094a1a4ead6%2Fp1gc7yq_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Calculating the Limit of \(\frac{\pi \sin \theta}{50 - 2 \sin \theta}\) as \(\theta \to 0\)
To find the limit of the expression \(\frac{\pi \sin \theta}{50 - 2 \sin \theta}\) as \(\theta\) approaches 0, follow these steps:
\[
\lim_{\theta \to 0} \frac{\pi \sin \theta}{50 - 2 \sin \theta}
\]
### Step-by-Step Calculation:
1. **Substitute \(\theta = 0\):**
Substitute \(\theta = 0\) directly into the equation:
\[
\frac{\pi \sin(0)}{50 - 2 \sin(0)} = \frac{\pi \cdot 0}{50 - 2 \cdot 0} = \frac{0}{50} = 0
\]
Therefore, the limit of \(\frac{\pi \sin \theta}{50 - 2 \sin \theta}\) as \(\theta\) approaches 0 is:
\[
\boxed{0}
\]
This shows that the value of the expression approaches 0 as \(\theta\) gets closer to 0.
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