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

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Chapter 7.3, Problem 16E
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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 Domain and Range of a Function In Exercises 15-30, find the domain and range of the function. See Example 2.

z = 4 − x 2 − y 2

To determine

The domain and range of the function z=4−x2−y2.

Explanation

Given Information:

For the function z=4−x2−y2,x  and  y are independent variables and z is the dependent variable.

Domain represents the set of values for which the function exists and range represents the set of output values of the function starting from minimum value to the maximum value.

Thus, first observe the domain of the function then correspondingly find its range.

Consider the given function,

z=4−x2−y2

As quantity inside the root must be non-negative so 4−x2−y2≥0

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Chapter 7.3,
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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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P-2SWUSect-7.7 P-3SWUSect-7.7 P-4SWUSect-7.7 P-5SWUSect-7.7 P-6SWUSect-7.7 P-7SWUSect-7.7 P-8SWUSect-7.7 P-1ESect-7.7 P-2ESect-7.7 P-3ESect-7.7 P-4ESect-7.7 P-5ESect-7.7 P-6ESect-7.7 P-7ESect-7.7 P-8ESect-7.7 P-9ESect-7.7 P-10ESect-7.7 P-11ESect-7.7 P-12ESect-7.7 P-13ESect-7.7 P-14ESect-7.7 P-15ESect-7.7 P-16ESect-7.7 P-17ESect-7.7 P-18ESect-7.7 P-19ESect-7.7 P-20ESect-7.7 P-21ESect-7.7 P-22ESect-7.7 P-23ESect-7.7 P-24ESect-7.7 P-25ESect-7.7 P-26ESect-7.7 P-27ESect-7.7 P-28ESect-7.7 P-29ESect-7.7 P-30ESect-7.8 P-1CPSect-7.8 P-2CPSect-7.8 P-3CPSect-7.8 P-4CPSect-7.8 P-5CPSect-7.8 P-6CPSect-7.8 P-1SWUSect-7.8 P-2SWUSect-7.8 P-3SWUSect-7.8 P-4SWUSect-7.8 P-5SWUSect-7.8 P-6SWUSect-7.8 P-7SWUSect-7.8 P-8SWUSect-7.8 P-9SWUSect-7.8 P-10SWUSect-7.8 P-11SWUSect-7.8 P-12SWUSect-7.8 P-13SWUSect-7.8 P-14SWUSect-7.8 P-15SWUSect-7.8 P-16SWUSect-7.8 P-1ESect-7.8 P-2ESect-7.8 P-3ESect-7.8 P-4ESect-7.8 P-5ESect-7.8 P-6ESect-7.8 P-7ESect-7.8 P-8ESect-7.8 P-9ESect-7.8 P-10ESect-7.8 P-11ESect-7.8 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Single Variable Calculus: Early Transcendentals

Compute the principal for the following loans. Use ordinary interest when time is stated in days. Principal Rat...

Contemporary Mathematics for Business & Consumers

Find the period of a wave whose frequency is 5.0 kHz.

Elementary Technical Mathematics

Draw vectors representing the following velocities: 30 mi/hr due west

Trigonometry (MindTap Course List)

In Exercises 27 to 30, find the area of the figure shown. Given: Hexagon RSTVWX with WV-XT-RS- RS=10 ST=8 TV=5 ...

Elementary Geometry For College Students, 7e

Show that each of the following polynomials is irreducible over the field of rational numbers by making the app...

Elements Of Modern Algebra

Using the Definition of Limit In Exercises 47-58, find the limit L. Then use the definition to prove that the...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding a Derivative In Exercises 9-20, use the rules of differentiation to find the derivative of the function...

Calculus of a Single Variable

HOME SALES KR Builders build three models of houses, M1, M2, and M3 in three subdivisions I, II, and III locate...

Finite Mathematics for the Managerial, Life, and Social Sciences

Given: mAB=92mDA=114mBC=138 Find: a)m1(DAC)b)m2(ADB)c)m3(AFB)d)m4(DEC)e)m5(CEB)

Elementary Geometry for College Students

Graphing a Function Using Technology In Exercises 43-46, use a computer algebra system to graph the function. f...

Multivariable Calculus

PUTNAM EXAM CHALLENGE If a0,a1,,an are real numbers satisfying a01+a12++ann+1=0 show that the equation a0+a1x+a...

Calculus

Let S be the surface of the closed cylindrical “half can” and F(x, y, z) = 2xy2i + xz2j + yzk. Write a triple i...

Study Guide for Stewart's Multivariable Calculus, 8th

Suppose . Then F(x)g(x) + C f′(g(x)) + C F(g′(x)) + C F(g(x)) + C

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

Finding a Limit Using a Definite Integral Find limxi=1nsin(i/n)n by evaluating an appropriate definite integral...

Calculus (MindTap Course List)

Identify the strengths and weaknesses of an ABAB reversal design and describe the circumstances in which it sho...

Research Methods for the Behavioral Sciences (MindTap Course List)

A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuro...

Introduction To Statistics And Data Analysis

Find the unknown area, radius, or central angle for each of these sectors 25 through 36. Where necessary, round...

Mathematics For Machine Technology

Identify the appropriate statistical test for each of the following nonexperimental and quasi-experimental desi...

Research Methods for the Behavioral Sciences (MindTap Course List)

The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opi...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Critical Thinking Determine if the statement is true or false. If the statement is false, then correct it and m...

College Algebra (MindTap Course List)

The Cond Nast Traveler Gold List provides ratings for the top 20 small cruise ships. The data shown below are t...

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

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