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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7.9, Problem 1E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding the Volume of a Solid Region In Exercises 1-6, find the volume of the solid region bounded in the first octant by the plane. See Example 1.

z = 5 − x − y

To determine

To calculate: The volume of solid region bounded in first octane and the plane z=5−x−y.

Explanation

Given information:

The provided equation of plane is z=5−x−y.

Formula used:

The procedure to calculate volume of surface z=f(x,y),

Step-1: Write the equation of surface in the form z=f(x,y)

Step-2: Sketch the projected region R in the x-y-plane.

Step-3: Determine the order of limits of integration.

Step-4: Evaluate the volume of solid region,

Volume=∫mn∫abf(x,y)dxdy

Here, the projected region is R:

m≤y≤n and a≤x≤b

Calculation:

Consider equation of plane,

z=5−x−y

The following table shown different coordinate of (x,y,z) for z=5−x−y.

x-Coordinate y-Coordinate z-Coordinate (x,y,z) Coordinate
0 0 5 (0,0,5)
0 5 0 (0,5,0)
5 0 0 (5,0,0)

The graph of function z=5−x−y in first octant shown below.

Substitute, 0 for z in equation of plane z=5−x−y.

5−x−y=0x+y=5

The region R is bounded by the line x=0,y=0 and y=5−x.

The following table shown different coordinate of (x,y) for x+y=5.

x-Coordinate y-Coordinate (x,y) Coordinate
0 5 (5,0)
5 0 (0,5)

The sketch of region R: x+y=5 in the xy-plane.

One way to set up the double integration is to choose x as the outer variable with that choice. The bounds for x are 0≤x≤5 and bounds for y are 0≤y≤5−x and another choose to set up the double integration is to choose y as the outer variable. with that choice, The bounds for y are 0≤y≤5 and bounds for x are 0≤x≤5−y

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
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Statistics for The Behavioral Sciences (MindTap Course List)

Statistical Literacy A data set has values ranging from a low of 10 to a high of 50. What's wrong with using th...

Understanding Basic Statistics

Researchers measured the blood alcohol concentration (BAC) of eight adult male subjects after rapid consumption...

Single Variable Calculus

The difference of two sets,, is defined as the set containing all elements of except those in .That is .Find ...

Mathematical Applications for the Management, Life, and Social Sciences

For Problems 1-50, solve each equation. Objective 1 6y7=41

Intermediate Algebra

In Example 6.8, we introduced the concept of a censored experiment in which n components are put on test and th...

Probability and Statistics for Engineering and the Sciences

Evaluate the expression sin Exercises 116. 323

Finite Mathematics

Write the ordered pair corresponding to each point in Illustration I: ILLUSTRATION 1 J

Elementary Technical Mathematics

Solve for x in each of the following right triangles:

Trigonometry (MindTap Course List)

As an accountant for the Give Me A Break Tax Service, use the Tax Table, Exhibit 18-3, or the Tax Computation W...

Contemporary Mathematics for Business & Consumers

34. Let be a subgroup of with index . a. Prove that is a normal subgroup of . b. Prove that...

Elements Of Modern Algebra

Search Engine Rankings The following circle graph shows the percent of the 18.6 billion U.S. searches that were...

Mathematical Excursions (MindTap Course List)

In Exercises 17 to 22, use proportions to solve each problem. Assume that AB is the geometric mean of BD and BC...

Elementary Geometry For College Students, 7e

Approximating an Integral In Exercises 63 - 70, use a power series to approximate the value of the integral wit...

Calculus: Early Transcendental Functions (MindTap Course List)

(a) Write an expression for a Riemann sum of a function f. Explain the meaning of the notation that you use. (b...

Single Variable Calculus: Early Transcendentals

Finding an Indefinite Integral In Exercises 75-82, find the indefinite integral using the formulas from Theorem...

Calculus of a Single Variable

In Exercise 71-80, determine whether the statement is true or false. If it is true explain why it is true. If i...

Finite Mathematics for the Managerial, Life, and Social Sciences

For the five-pointed star a regular pentagram inscribed in the circle, find the measure of 1and2.

Elementary Geometry for College Students

Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

Calculus

converges to: 2 the series diverges

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: n=1an converges if and only if limnan=0.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Area: In Exercises 4752, sketch a graph of the region bounded by the graphs of the equations. Then use a double...

Multivariable Calculus

Determine the roots of the following terms. 16x4y84

Mathematics For Machine Technology

Describe the purpose for control conditions in experimental research, define the two basic types of control con...

Research Methods for the Behavioral Sciences (MindTap Course List)

In baseball, an earned run is any run that the opposing team scores off the pitcher except for runs scored as a...

Statistics for Business & Economics, Revised (MindTap Course List)

Find the value ofb, if any, that would cause the graph of fx=logbx to look like the graph shown.

College Algebra (MindTap Course List)

Both surface soil and subsoil specimens were taken from eight randomly selected agricultural locations in a par...

Introduction To Statistics And Data Analysis

An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe how the reliability of a personality test could be established using the results from a correlational ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Finding a Limit In Exercises 11-28, Find the limit. limx0(5x3)

Calculus (MindTap Course List)

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