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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Question
I need help with the polar curve, the area enclosed by the Polar curve will be topics that I need to cover. Can you please describe step by step and whatever methods you are using for me to understand it better and fully grasp it? This is one of my practice questions. Also please draw the polar curves.
![### Equation
The equation shown in the image is:
\[ r = \ln(\theta), \quad \text{for } \theta \geq 1 \]
### Explanation
This equation represents a curve in polar coordinates, where \( r \) is the radial distance from the origin, and \( \theta \) is the angle in radians. The function \( \ln(\theta) \) indicates that the radial distance is determined by the natural logarithm of the angle \( \theta \).
### Graph Description
In this context, a graph of this equation for \( \theta \geq 1 \) would illustrate how the radial distance \( r \) increases logarithmically as \( \theta \) increases. The curve would start at \( \theta = 1 \) and extend outward, with the growth slowing as \( \theta \) becomes larger, reflecting the properties of the logarithmic function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff62d5ca7-5439-4cfe-bb83-29d1381eaedb%2F498ba93d-9bed-436a-bdec-75c09366d511%2F1p3wk1_processed.png&w=3840&q=75)
Transcribed Image Text:### Equation
The equation shown in the image is:
\[ r = \ln(\theta), \quad \text{for } \theta \geq 1 \]
### Explanation
This equation represents a curve in polar coordinates, where \( r \) is the radial distance from the origin, and \( \theta \) is the angle in radians. The function \( \ln(\theta) \) indicates that the radial distance is determined by the natural logarithm of the angle \( \theta \).
### Graph Description
In this context, a graph of this equation for \( \theta \geq 1 \) would illustrate how the radial distance \( r \) increases logarithmically as \( \theta \) increases. The curve would start at \( \theta = 1 \) and extend outward, with the growth slowing as \( \theta \) becomes larger, reflecting the properties of the logarithmic function.
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