Explanation Let the interval [ a , b ] be divided into n subintervals each of width h . Then, average value of f on [ a , b ] for the n subintervals and the given choices of x i is, A = ∑ i = 1 n f ( x i ) n = b − a b − a ( ∑ i = 1 n f ( x i ) n ) = 1 b − a ∑ i = 1 n f ( x i ) ( b − a n ) = 1 b − a ∑ i = 1 n f ( x i ) h Take limit as n → ∞ .

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

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The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 8.CR, Problem 7CR

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To state:

If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.

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Chapter 8.CR, Problem 6CR

Chapter 8.CR, Problem 8CR

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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.

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(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).

Chapter 8 Solutions

Calculus For The Life Sciences

Ch. 8.1 - YOUR TURN Use the trapezoidal rule with n=4 to...Ch. 8.1 - Prob. 2YT Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E

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To state: If average value of the function f on [ 1 , 4 ] is given by 1 3 ∫ 1 4 π ( 2 x 2 + 3 ) 2 d x is true or false.

Solution Summary: The author states that if the function f is given by 13displaystyle, it is true or false.

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To state:

If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.

Want to see the full answer?

Chapter 8 Solutions

To state: If average value of the function f on [ 1 , 4 ] is given by 1 3 ∫ 1 4 π ( 2 x 2 + 3 ) 2 d x is true or false.

Solution Summary: The author states that if the function f is given by 13displaystyle, it is true or false.

Concept explainers

Videos

To state: If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.

Want to see the full answer?

Chapter 8 Solutions

To state:

If average value of the function f on [1,4] is given by 13∫14π(2x2+3)2dx is true or false.