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...
Related questions
Question
![**Problem Statement:**
Find the slope of the tangent line to the given polar curve at the point specified by the value of \( \theta \).
Given:
\[ r = \sin(\theta) + 3 \cos(\theta), \quad \theta = \frac{\pi}{2} \]
**Solution Approach:**
1. To find the slope of the tangent line for the polar curve \( r \) in terms of \( \theta \), follow the general steps for finding the derivative in polar coordinates.
2. Use the given value of \( \theta = \frac{\pi}{2} \) to evaluate the function.
In the provided image, solving the problem results in an incorrect answer, as indicated by the red cross. The fraction shown as:
\[ \frac{1}{3} \]
This indicates a potential mistake was made during the calculation process. Ensure to review steps and derivatives in polar coordinates to arrive at the correct solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faea7a391-77a2-4be9-b3a3-98e0f70bf810%2F52b5ea77-565f-4ad9-9693-9d6e42da8568%2Fcsafxk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the slope of the tangent line to the given polar curve at the point specified by the value of \( \theta \).
Given:
\[ r = \sin(\theta) + 3 \cos(\theta), \quad \theta = \frac{\pi}{2} \]
**Solution Approach:**
1. To find the slope of the tangent line for the polar curve \( r \) in terms of \( \theta \), follow the general steps for finding the derivative in polar coordinates.
2. Use the given value of \( \theta = \frac{\pi}{2} \) to evaluate the function.
In the provided image, solving the problem results in an incorrect answer, as indicated by the red cross. The fraction shown as:
\[ \frac{1}{3} \]
This indicates a potential mistake was made during the calculation process. Ensure to review steps and derivatives in polar coordinates to arrive at the correct solution.
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