Vr2 – x², whose graph is the 6. Let r > 0 be a real number. Suppose y semi-circle of radius r about the origin. f(x) upper || (a) Calculate and simplify the expressions V1+ f'(x)² and f(x)/1+ f'(x)². (b) Suppose -r < a < b < r. Calculate the surface area of the portion of the sphere of radius r between x = a and x = b. (c) Imagine cutting a spherical orange by equidistant parallel planes. (An orange cut into nine equal-width pieces is shown.) Which pieces do you expect to have the most rind: Those near "the poles", or those near "the equator"? How does your intuition compare with the result of (b)?
Vr2 – x², whose graph is the 6. Let r > 0 be a real number. Suppose y semi-circle of radius r about the origin. f(x) upper || (a) Calculate and simplify the expressions V1+ f'(x)² and f(x)/1+ f'(x)². (b) Suppose -r < a < b < r. Calculate the surface area of the portion of the sphere of radius r between x = a and x = b. (c) Imagine cutting a spherical orange by equidistant parallel planes. (An orange cut into nine equal-width pieces is shown.) Which pieces do you expect to have the most rind: Those near "the poles", or those near "the equator"? How does your intuition compare with the result of (b)?
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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Transcribed Image Text:Vr2 – x², whose graph is the upper
6. Let r > 0 be a real number. Suppose y
semi-circle of radius r about the origin.
f(x)
(a) Calculate and simplify the expressions /1+ f'(x)² and f(x)/1+ f"(x)².
(b) Suppose -r < a < b < r. Calculate the surface area of the portion of the sphere of
radius r between x = a and x = b.
(c) Imagine cutting a spherical orange by equidistant parallel planes. (An orange cut into
nine equal-width pieces is shown.) Which pieces do you expect to have the most rind:
Those near "the poles", or those near "the equator"? How does your intuition compare
with the result of (b)?
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