Explanation Given info: f ( x , y , z ) = e x + y + z ; W: 0 ≤ z ≤ 1 , 0 ≤ y ≤ x , 0 ≤ x ≤ 1 Concept used: First perform integration with respect to x , after that either with respect to y or z . Calculation: ∭ w ( x , y , z ) dv W: 0 ≤ z ≤ 1 , 0 ≤ y ≤ x , 0 ≤ x ≤ 1 W: 0 ≤ z ≤ 1 , 0 ≤ x ≤ 1 , 0 ≤ y ≤ x Put the limit in same order = ∫ 0 1 ∫ 0 1 ∫ 0 x e x + y + 2 d y d x d z ( putting the value of function and limit ) ( use e x + y + 2 = e x . e y . e z ) = ∫ 0 1 ∫ 0 1 ∫ 0 x e x . e y . e z . d y d x d z ( first integrate w .r .t to y, assume x and y as constant ) = ∫ 0 1 ∫ 0 1 ∫ 0 x ( e x e z ) ( e y d y ) d x d z ( ∫ 0 x e y . d y = [ e y ] 0 x = ( e x − 1 ) ) = ∫ 0 1 ∫ 00 1 e x . e z [ ( e y ) ] 0 x d x d z ( rewrite the expression ) Putting the value of limit ∫ 0 1 ∫ 0 1 e x . e z ( e x − 1 ) d x d z ( Integrate w .r .t x keeping z as constant ) = ∫ 0 1 ∫ 0 1 e z ( ( e x . e x − e x ) d x ) d z = ∫ 0 1 ∫ 0 1 e z ( e 2 x − e x ) d x d z = ∫ 0 1 e z [ e 2 x 2 − e x ] 0 1 d z ( ∫ ( e 2 x − e x ) d x = ( e 2 x 2 − e x ) ) = ∫ 0 1 e z { ( e 2...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Question

Chapter 16.3, Problem 10E

To determine

Evaluate $\underset{w}{∭} f (x, y, z) dv$ for the function and region $W$ specified $f (x, y, z) = e^{x + y + z}; W: 0 \leq z \leq 1, 0 \leq y \leq x, 0 \leq x \leq 1$

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Chapter 16.3, Problem 9E

Chapter 16.3, Problem 11E

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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Evaluate ∭ w f ( x , y , z ) dv for the function and region W specified f ( x , y , z ) = e x + y + z ; W: 0 ≤ z ≤ 1 , 0 ≤ y ≤ x , 0 ≤ x ≤ 1

Solution Summary: The author evaluates w f ( x, y. z ) dv for the function and region W, and puts the limit in same order.

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Evaluate $\underset{w}{∭} f (x, y, z) dv$ for the function and region $W$ specified $f (x, y, z) = e^{x + y + z}; W: 0 \leq z \leq 1, 0 \leq y \leq x, 0 \leq x \leq 1$

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Chapter 16 Solutions

Evaluate ∭ w f ( x , y , z ) dv for the function and region W specified f ( x , y , z ) = e x + y + z ; W: 0 ≤ z ≤ 1 , 0 ≤ y ≤ x , 0 ≤ x ≤ 1

Solution Summary: The author evaluates w f ( x, y. z ) dv for the function and region W, and puts the limit in same order.

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Evaluate ∭wf(x,y,z) dv for the function and region Wspecified f(x,y,z)=ex+y+z; W: 0≤z≤1, 0≤y≤x, 0≤x≤1

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Chapter 16 Solutions

Evaluate $\underset{w}{∭} f (x, y, z) dv$ for the function and region $W$ specified $f (x, y, z) = e^{x + y + z}; W: 0 \leq z \leq 1, 0 \leq y \leq x, 0 \leq x \leq 1$