Explanation Approach: If there is a surface z define as z = f ( x , y ) and the region R as a ≤ x ≤ b , c ≤ y ≤ d , then the volume ( V ) of the surface over the rectangular region R is V = ∬ R f ( x , y ) d x d y = ∫ c d ∫ a b f ( x , y ) d x d y . Calculation: Given, the surface z = 3 x + 10 y + 20 and the boundaries is 0 ≤ x ≤ 3 , − 2 ≤ y ≤ 1 . Volume of the surface over the rectangular region is, V = ∫ − 2 1 ∫ 0 3 ( 3 x + 10 y + 20 ) d x d y = ∫ − 2 1 [ 3 x 2 2 + 10 x y + 20 x ] 0 3 d y = ∫ − 2 1 [

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ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 9.5, Problem 32E

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To find:

The volume of the surface z=3x+10y+20 above the rectangle with the boundaries 0≤x≤3,−2≤y≤1.

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Chapter 9.5, Problem 31E

Chapter 9.5, Problem 33E

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4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of about

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The volume of the surface z = 3 x + 10 y + 20 above the rectangle with the boundaries 0 ≤ x ≤ 3 , − 2 ≤ y ≤ 1 .

Solution Summary: The author calculates the volume of the surface z=3x+10y+20 above the rectangle with the boundaries.

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To find:

The volume of the surface z=3x+10y+20 above the rectangle with the boundaries 0≤x≤3,−2≤y≤1.

Want to see the full answer?

Chapter 9 Solutions

The volume of the surface z = 3 x + 10 y + 20 above the rectangle with the boundaries 0 ≤ x ≤ 3 , − 2 ≤ y ≤ 1 .

Solution Summary: The author calculates the volume of the surface z=3x+10y+20 above the rectangle with the boundaries.

Concept explainers

Videos

To find: The volume of the surface z=3x+10y+20 above the rectangle with the boundaries 0≤x≤3,−2≤y≤1.

Want to see the full answer?

Chapter 9 Solutions

To find:

The volume of the surface z=3x+10y+20 above the rectangle with the boundaries 0≤x≤3,−2≤y≤1.