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=h² (3r-h), for 0shsr. Complete parts (a)-(d). The volume of the cap of a sphere of radius r and thickness h is V= a. Compute the partial derivatives V₁, and V₁. V₁-0 b. For a sphere of any radius, is the rate of change of volume with respect to r greater when h = 0.2r or when h=0.8r? The rate of change of volume with respect to r is greater when h = c. For a sphere of any radius, for what value of h is the rate of change of volume with respect to r equal to 1? The rate of change of volume with respect to r equals to 1 when h = (Type an exact answer, using it as needed.) d. For a fixed radius r, for what value of h (0 ≤ h≤r) is the rate of change of volume with respect to h the greatest? The rate of change of volume with respect to h is the greatest when h =

=h² (3r-h), for 0shsr. Complete parts (a)-(d). The volume of the cap of a sphere of radius r and thickness h is V= a. Compute the partial derivatives V₁, and V₁. V₁-0 b. For a sphere of any radius, is the rate of change of volume with respect to r greater when h = 0.2r or when h=0.8r? The rate of change of volume with respect to r is greater when h = c. For a sphere of any radius, for what value of h is the rate of change of volume with respect to r equal to 1? The rate of change of volume with respect to r equals to 1 when h = (Type an exact answer, using it as needed.) d. For a fixed radius r, for what value of h (0 ≤ h≤r) is the rate of change of volume with respect to h the greatest? The rate of change of volume with respect to h is the greatest when h =

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...
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14Please show the answer for each section clearly
=h² (3r-h), for 0shsr. Complete parts (a)-(d). The volume of the cap of a sphere of radius r and thickness h is V= a. Compute the partial derivatives V₁, and V₁. V₁-0 b. For a sphere of any radius, is the rate of change of volume with respect to r greater when h = 0.2r or when h=0.8r? The rate of change of volume with respect to r is greater when h = c. For a sphere of any radius, for what value of h is the rate of change of volume with respect to r equal to 1? The rate of change of volume with respect to r equals to 1 when h = (Type an exact answer, using it as needed.) d. For a fixed radius r, for what value of h (0 ≤h≤r) is the rate of change of volume with respect to h the greatest? The rate of change of volume with respect to h is the greatest when h =
Transcribed Image Text:=h² (3r-h), for 0shsr. Complete parts (a)-(d). The volume of the cap of a sphere of radius r and thickness h is V= a. Compute the partial derivatives V₁, and V₁. V₁-0 b. For a sphere of any radius, is the rate of change of volume with respect to r greater when h = 0.2r or when h=0.8r? The rate of change of volume with respect to r is greater when h = c. For a sphere of any radius, for what value of h is the rate of change of volume with respect to r equal to 1? The rate of change of volume with respect to r equals to 1 when h = (Type an exact answer, using it as needed.) d. For a fixed radius r, for what value of h (0 ≤h≤r) is the rate of change of volume with respect to h the greatest? The rate of change of volume with respect to h is the greatest when h =
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