Explanation Given information: A statement is given as - "If f ( 0 ) = 0 and f ( 10 ) = 50 , then the average value of f on the interval 0 ≤ x ≤ 10 is between 0 and 50 ." Calculation: A statement is given as - A statement is given as - "If f ( 0 ) = 0 and f ( 10 ) = 50 , then the average value of f on the interval 0 ≤ x ≤ 10 is between 0 and 50

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 5, Problem 52SYU

To determine

Whether the given statement is true or false.

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Chapter 5, Problem 51SYU

Chapter 5, Problem 53SYU

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(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.

(14 points) Let f: R3 R and T: R3. →R³ be defined by f(x, y, z) = ln(x²+ y²+2²), T(p, 0,4)=(psin cos 0, psin sin, pcos). (a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the gradient Vg directly, i.e. without using the chain rule. (b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4). (c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate Vg(r,0,4).

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APPLIED CALCULUS (WILEY PLUS)

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Whether the given statement is true or false.

Solution Summary: The author explains whether the given statement is true or false. Since there is no information about the function f(x), only boundary value is given.

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Whether the given statement is true or false.

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Chapter 5 Solutions