Part IV: Review Problem for Final (do if you have time or at home) 11. Let r= 6cos (50). Find the EXACT area of the region inside ONE petal but outside r = 3.
Part IV: Review Problem for Final (do if you have time or at home) 11. Let r= 6cos (50). Find the EXACT area of the region inside ONE petal but outside r = 3.
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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Part IV
![### Calculus Exercises for Students
#### Exercise e:
Find the limit along the path \(y = \sqrt{x}\).
---
#### Exercise f:
What can you now say about
\[
\lim_{(x,y) \to (0,0)} \frac{x^3y^2}{x^4 + y^8} ?
\]
---
### Part IV: Review Problem for Final (do if you have time or at home)
#### Problem 11:
Let \( r = 6 \cos(5\theta) \). Find the EXACT area of the region inside ONE petal but outside \( r = 3 \).
---
#### Explanation of Diagram
The diagram included shows a polar graph with multiple petals. The graph \( r = 6 \cos(5\theta) \) is a rose curve with 5 petals. The points where the curve crosses the axis form each petal. The problem requires identifying the exact area of the region inside one of these petals but outside the circle \( r = 3 \).
The intersection points of the outer curve \( r = 6 \cos(5\theta) \) and the inner circle \( r = 3 \) need to be calculated to find the integral boundaries for determining the area of the specified region.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3acae65-05d5-4940-8762-2c9a874e450a%2Fb52e8829-b144-45d9-b84c-b624344a1ae9%2F81mhvh7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Exercises for Students
#### Exercise e:
Find the limit along the path \(y = \sqrt{x}\).
---
#### Exercise f:
What can you now say about
\[
\lim_{(x,y) \to (0,0)} \frac{x^3y^2}{x^4 + y^8} ?
\]
---
### Part IV: Review Problem for Final (do if you have time or at home)
#### Problem 11:
Let \( r = 6 \cos(5\theta) \). Find the EXACT area of the region inside ONE petal but outside \( r = 3 \).
---
#### Explanation of Diagram
The diagram included shows a polar graph with multiple petals. The graph \( r = 6 \cos(5\theta) \) is a rose curve with 5 petals. The points where the curve crosses the axis form each petal. The problem requires identifying the exact area of the region inside one of these petals but outside the circle \( r = 3 \).
The intersection points of the outer curve \( r = 6 \cos(5\theta) \) and the inner circle \( r = 3 \) need to be calculated to find the integral boundaries for determining the area of the specified region.
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