Homework Help is Here – Start Your Trial Now!
Math
Calculus
The following is a sketch of an ellipse and part of a circle with radius =r. The equation of the ellipse in polar coordinates is r =: 10 3-2cose 1. Set your graphing calculator or Geogebra to Polar mode and plot the graph. Use equal scales on both x- and y-axes. Include your graph here. 2. Graph a sample point (r,0) at 0-0.3 radian. Calculate r, x, and y for this point. Show that all three agree with your graph. 3. The area of a wedge-shaped piece of the elliptical region bounded by the graph is approximately equal to the area of the sector of a circle. Calculate the area of the sector shown in the figure if 0=0.3 radian and do= 0.1 radian. 4. Show that in general, the area dA=rde 5. The exact area of the elliptical region is the limit of the sum of the sectors" areas. That is, the area equals the definite integral of dA. Write an integral representing the exact area. Evaluate the integral numerically.

The following is a sketch of an ellipse and part of a circle with radius =r. The equation of the ellipse in polar coordinates is r =: 10 3-2cose 1. Set your graphing calculator or Geogebra to Polar mode and plot the graph. Use equal scales on both x- and y-axes. Include your graph here. 2. Graph a sample point (r,0) at 0-0.3 radian. Calculate r, x, and y for this point. Show that all three agree with your graph. 3. The area of a wedge-shaped piece of the elliptical region bounded by the graph is approximately equal to the area of the sector of a circle. Calculate the area of the sector shown in the figure if 0=0.3 radian and do= 0.1 radian. 4. Show that in general, the area dA=rde 5. The exact area of the elliptical region is the limit of the sum of the sectors" areas. That is, the area equals the definite integral of dA. Write an integral representing the exact area. Evaluate the integral numerically.

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question

See attached images.

6. The x-radius, a, of the ellipse shown is 6 units. Measure or calculate the y-radius, b. Then confirm that the answer you got by integration in Part 5 agrees with the answer you get using the ellipse area formula A=nab. 7. Summarize of what you have learned from this activity in a one page document.
Transcribed Image Text:6. The x-radius, a, of the ellipse shown is 6 units. Measure or calculate the y-radius, b. Then confirm that the answer you got by integration in Part 5 agrees with the answer you get using the ellipse area formula A=nab. 7. Summarize of what you have learned from this activity in a one page document.
is, a, of the Then confirm that the you get using the ellips The following is a sketch of an ellipse and part of a circle with radius = r. The equation of the ellipse in polar coordinates is r = 10 7. Summarize of what you 3-2cose 1. Set your graphing calculator or Geogebra to Polar mode and plot the graph. Use equal scales on both x- and y-axes. Include your graph here. 2. Graph a sample point (r,O) at 0=0.3 radian. Calculate r, x, and y for this point. Show that all three agree with your graph. 3. The area of a wedge-shaped piece of the elliptical region bounded by the graph is approximately equal to the area of the sector of a circle. Calculate the area of the sector shown in the figure if 0=0.3 radian and dO= 0.1 radian. 4. Show that in general, the area dA=r 5. The exact area of the elliptical region is the limit of the sum of the sectors" areas. That is, the area equals the definite integral of dA. Write an integral representing the exact area. Evaluate the integral numerically.
Transcribed Image Text:is, a, of the Then confirm that the you get using the ellips The following is a sketch of an ellipse and part of a circle with radius = r. The equation of the ellipse in polar coordinates is r = 10 7. Summarize of what you 3-2cose 1. Set your graphing calculator or Geogebra to Polar mode and plot the graph. Use equal scales on both x- and y-axes. Include your graph here. 2. Graph a sample point (r,O) at 0=0.3 radian. Calculate r, x, and y for this point. Show that all three agree with your graph. 3. The area of a wedge-shaped piece of the elliptical region bounded by the graph is approximately equal to the area of the sector of a circle. Calculate the area of the sector shown in the figure if 0=0.3 radian and dO= 0.1 radian. 4. Show that in general, the area dA=r 5. The exact area of the elliptical region is the limit of the sum of the sectors" areas. That is, the area equals the definite integral of dA. Write an integral representing the exact area. Evaluate the integral numerically.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS