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

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Chapter 7.9, Problem 30E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Problem 2SWU
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Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
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Problem 17E
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Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
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Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Average Value of a Function over a Region In Exercises 27–30, find the average value of f(x, y) over the region R.

f ( x , y ) = e x + y

R: triangle with vertices (0, 0), (0, 1), (1, 1)

To determine

To calculate: The average value of f(x,y)=ex+y over the region R: square with triangle

(0,0),(0,1),(1,1).

Explanation

Given information:

The provided function is f(x,y)=ex+y.

The region R: triangle with vertices (0,0),(0,1),(1,1).

Formula used:

The average value of integrable function z=f(x,y) over the region R with area A is;

Average value=1A∬Rf(x,y)dxdy

Calculation:

Consider equation of function,

f(x,y)=ex+y

The region R: triangle with vertices (0,0),(0,1),(1,1).

The area of region R is 12 square units.

Now apply, the formula of the average value of integrable function f(x,y)=ex+y over the region triangle with vertices (0,0),(0,1),(1,1) with area 12 units is

Average value=2∫01∫0y(ex+y)dxdy

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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
Sect-7.1 P-4SWUSect-7.1 P-5SWUSect-7.1 P-6SWUSect-7.1 P-7SWUSect-7.1 P-8SWUSect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.1 P-8ESect-7.1 P-9ESect-7.1 P-10ESect-7.1 P-11ESect-7.1 P-12ESect-7.1 P-13ESect-7.1 P-14ESect-7.1 P-15ESect-7.1 P-16ESect-7.1 P-17ESect-7.1 P-18ESect-7.1 P-19ESect-7.1 P-20ESect-7.1 P-21ESect-7.1 P-22ESect-7.1 P-23ESect-7.1 P-24ESect-7.1 P-25ESect-7.1 P-26ESect-7.1 P-27ESect-7.1 P-28ESect-7.1 P-29ESect-7.1 P-30ESect-7.1 P-31ESect-7.1 P-32ESect-7.1 P-33ESect-7.1 P-34ESect-7.1 P-35ESect-7.1 P-36ESect-7.1 P-37ESect-7.1 P-38ESect-7.1 P-39ESect-7.1 P-40ESect-7.1 P-41ESect-7.1 P-42ESect-7.1 P-43ESect-7.1 P-44ESect-7.2 P-1CPSect-7.2 P-2CPSect-7.2 P-3CPSect-7.2 P-1SWUSect-7.2 P-2SWUSect-7.2 P-3SWUSect-7.2 P-4SWUSect-7.2 P-5SWUSect-7.2 P-6SWUSect-7.2 P-1ESect-7.2 P-2ESect-7.2 P-3ESect-7.2 P-4ESect-7.2 P-5ESect-7.2 P-6ESect-7.2 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10ESect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 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For Review Exercises 21 to 23, DEAC BD=6,BE=8,EC=4,AD=?

Elementary Geometry For College Students, 7e

The problems that follow review material we covered in Section 4.3. Graph one complete cycle. y=cos(x3)

Trigonometry (MindTap Course List)

For Octoberfest, a vender purchased 15 kg of German brats. How many 6-oz brats can be made from the 15 kg of Ge...

Elementary Technical Mathematics

Use the percentage method of income tax calculation to complete the following payroll roster. Marital Withhold...

Contemporary Mathematics for Business & Consumers

If f(x) and g(x) are polynomials over the field F, and p(x)=f(x)g(x), prove that p(c)=f(c)g(c) for all c in F.

Elements Of Modern Algebra

Evaluating a Definite Integral In Exercises 23-34, evaluate the definite integral. 01/2arcsinx1x2dx

Calculus: Early Transcendental Functions (MindTap Course List)

Proof Prove that the tangent of the angle (0/2) between the radial line and the tangent line at the point (r, )...

Calculus of a Single Variable

In Exercise 6-11, draw the network corresponding to the logic statement. [p(qr)]q

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 1 to 6, simplify by combining similar terms. 3(2x+5)2(3x1)

Elementary Geometry for College Students

For f(x) = 5x2 + 1 the slope of the secant line between the points corresponding to x = 3 and x = 4 is: a) 7 b)...

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

Applying the First Derivative Test In Exercises 41-48, consider the function on the interval (0,2) . (a) Find t...

Calculus (MindTap Course List)

HOE DO YOU SEE IT?Using the graph, is 05f(x)dx positive or negative? Explain.

Calculus

Finding an Equation of a Plane In Exercises 41-44, find an equation of the plane with the given characteristics...

Multivariable Calculus

fx(a, b) is the slope of the tangent line to the curve formed by the intersection of the surface z = f(x, y) at...

Study Guide for Stewart's Multivariable Calculus, 8th

Data from a large study carried out in 2008 were used to estimate that 10% of all smokers who quit smoking are ...

Introduction To Statistics And Data Analysis

Determine whether each of the following hypotheses is testable and refutable. If not, explain why. The color re...

Research Methods for the Behavioral Sciences (MindTap Course List)

To lest for any significant difference in the number of hours between breakdowns for four machines, the followi...

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

Graph each polynomial function. f(x)=x54x3

College Algebra (MindTap Course List)

Find each percentage. Round the answers to 2 decimal places when necessary. 8. 2.15% of 80

Mathematics For Machine Technology

Due to a recent decline in the housing market, the national median sales price for single-family homes is 180,0...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Select one construct from the following list: happiness Hunger Exhaustion motivation creativity Fear Briefly de...

Research Methods for the Behavioral Sciences (MindTap Course List)

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