Explanation Given information: The statement is “If the curve y = f x , a ≤ x ≤ b , lies above the x − axis and if c > 0 , then the areas of the surfaces obtained by revolving y = f x and y = f x + c about the x − axis are equal.” Consider the real values function which involves the independent variable x as follows: y = f x = 1 Observe that the function y = f x has no x − intercept. Consider another real values function which also involves the independent variable x such as follows: y = f ( x ) + c = f ( x ) + 2 = 1 + 2 = 3 Observe that the function y = f x + c has the x − intercept as the c = 2 value. Both the functions of equations y = 1 , y = 3 operates in the interval a , b , such that it follows: a ≤ x ≤ b Observe the statement of the question and compare the functions of equations y = 1 , y = 3 The rotation of the function y = f x = 1 about the x − axis over the interval of 0 , 2 yields an open cylinder with radius of 1 unit and height of 2 units

9th Edition

ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

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Question

Chapter 8, Problem 2TFQ

To determine

To state: The statement “If the curve y=fx,a⩽x⩽b , lies above the x− axis and if c>0 , then the areas of the surfaces obtained by revolving y=fx and y=fx+c about the x− axis are equal.” is true or false.

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Chapter 8, Problem 1TFQ

Chapter 8, Problem 3TFQ

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Chapter 8 Solutions

Calculus, Early Transcendentals

Ch. 8.1 - Use the arc length formula (3) to find the length...Ch. 8.1 - Use the arc length formula to find the length of...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Find the exact length of the curve. 9....Ch. 8.1 - Find the exact length of the curve. 10....

Knowledge Booster

To state: The statement “If the curve y = f x , a ⩽ x ⩽ b , lies above the x − axis and if c > 0 , then the areas of the surfaces obtained by revolving y = f x and y = f x + c about the x − axis are equal.” is true or false.

Solution Summary: The author explains that the statement "If the curve y=f(x),ale

To state: The statement “If the curve y=fx,a⩽x⩽b , lies above the x− axis and if c>0 , then the areas of the surfaces obtained by revolving y=fx and y=fx+c about the x− axis are equal.” is true or false.

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Chapter 8 Solutions

To state: The statement “If the curve y = f x , a ⩽ x ⩽ b , lies above the x − axis and if c &gt; 0 , then the areas of the surfaces obtained by revolving y = f x and y = f x + c about the x − axis are equal.” is true or false.

Solution Summary: The author explains that the statement "If the curve y=f(x),ale

To state: The statement “If the curve y=fx,a⩽x⩽b , lies above the x− axis and if c>0 , then the areas of the surfaces obtained by revolving y=fx and y=fx+c about the x− axis are equal.” is true or false.

Want to see the full answer?

Chapter 8 Solutions

To state: The statement “If the curve y = f x , a ⩽ x ⩽ b , lies above the x − axis and if c > 0 , then the areas of the surfaces obtained by revolving y = f x and y = f x + c about the x − axis are equal.” is true or false.