Duvnit via Cillall 1. Consider the lune enclosed between x² +y² = 1 and x² +(y+1)² = 2. Show the following using calculus. If you wish you may use any computer algebra system you like to do the integrals, just write down each integral and its solution. I 0.5 III II -1 -0.5 a. Use calculus to show that the tangent line to x² +(y+1)² =2 at the point (-1,0) goes through (0,1). b. Use calculus to show that the area in region I on the graph is equal to half the area of region III. c. Find the area of the lune using calculus. d. Find the area of the lune using Hippocrates' solution. [Naturally, the answers to c and d should be the same.] 0.5
Duvnit via Cillall 1. Consider the lune enclosed between x² +y² = 1 and x² +(y+1)² = 2. Show the following using calculus. If you wish you may use any computer algebra system you like to do the integrals, just write down each integral and its solution. I 0.5 III II -1 -0.5 a. Use calculus to show that the tangent line to x² +(y+1)² =2 at the point (-1,0) goes through (0,1). b. Use calculus to show that the area in region I on the graph is equal to half the area of region III. c. Find the area of the lune using calculus. d. Find the area of the lune using Hippocrates' solution. [Naturally, the answers to c and d should be the same.] 0.5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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History of mathematics
Hippocrates’ Lunes
![1. Consider the lune enclosed between x² + y² =1 and x² + (y+1)² =2.
Show the following using calculus. If you wish
you may use any computer algebra system you
like to do the integrals, just write down each
integral and its solution.
I
0.5
III
II
-1
-0.5
a. Use calculus to show that the tangent line to x² + (y+1)² = 2 at the point (-1,0) goes through (0,1).
b. Use calculus to show that the area in region I on the graph is equal to half the area of region III.
c. Find the area of the lune using calculus.
d. Find the area of the lune using Hippocrates' solution.
[Naturally, the answers to c and d should be the same.]
0.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda859fed-ae51-422c-9773-627805a70b82%2Fd3f7ddb6-012a-4761-a1e3-22b20eb6e7fd%2Fuh9s9es_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the lune enclosed between x² + y² =1 and x² + (y+1)² =2.
Show the following using calculus. If you wish
you may use any computer algebra system you
like to do the integrals, just write down each
integral and its solution.
I
0.5
III
II
-1
-0.5
a. Use calculus to show that the tangent line to x² + (y+1)² = 2 at the point (-1,0) goes through (0,1).
b. Use calculus to show that the area in region I on the graph is equal to half the area of region III.
c. Find the area of the lune using calculus.
d. Find the area of the lune using Hippocrates' solution.
[Naturally, the answers to c and d should be the same.]
0.5
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