BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Sketch the region bounded by the paraboloids z = x2 + y2 and z = 2 − x2y2.

To determine

To sketch: The region bounded by the paraboloids z=x2+y2 and z=2x2y2 .

Explanation

Given data:

Paraboloid equations are z=x2+y2 and z=2x2y2 .

Formula used:

Consider the standard equation of an elliptic paraboloid along the z axis.

zc=x2a2+y2b2 (1)

Consider the given surface equation.

z=x2+y2 (2)

Modify the equation as follows.

z1=x21+y21 (3)

By comparing equation (3) with (1), the given surface equation satisfies the equation of an elliptic paraboloid along the z axis.

Find a, b, and c by comparing equation (3) with equation (1).

a2=1a=1a=±1

The value of a is ±1 .

b2=1b=1b=±1

The value of b is ±1 .

c=1

The value of c is 1.

Case i:

Let x=k .

Substitute k for x in equation (1),

z=k2+y2

The trace of this expression represents a parabola in the positive z direction.

Case ii:

Let y=k

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 12 Solutions

Show all chapter solutions add
Sect-12.1 P-11ESect-12.1 P-12ESect-12.1 P-13ESect-12.1 P-14ESect-12.1 P-15ESect-12.1 P-16ESect-12.1 P-17ESect-12.1 P-18ESect-12.1 P-19ESect-12.1 P-20ESect-12.1 P-21ESect-12.1 P-22ESect-12.1 P-23ESect-12.1 P-24ESect-12.1 P-25ESect-12.1 P-26ESect-12.1 P-27ESect-12.1 P-28ESect-12.1 P-29ESect-12.1 P-30ESect-12.1 P-31ESect-12.1 P-32ESect-12.1 P-33ESect-12.1 P-34ESect-12.1 P-35ESect-12.1 P-36ESect-12.1 P-37ESect-12.1 P-38ESect-12.1 P-39ESect-12.1 P-40ESect-12.1 P-41ESect-12.1 P-42ESect-12.1 P-43ESect-12.1 P-44ESect-12.1 P-45ESect-12.1 P-46ESect-12.1 P-47ESect-12.1 P-48ESect-12.2 P-1ESect-12.2 P-2ESect-12.2 P-3ESect-12.2 P-4ESect-12.2 P-5ESect-12.2 P-6ESect-12.2 P-7ESect-12.2 P-8ESect-12.2 P-9ESect-12.2 P-10ESect-12.2 P-11ESect-12.2 P-12ESect-12.2 P-13ESect-12.2 P-14ESect-12.2 P-15ESect-12.2 P-16ESect-12.2 P-17ESect-12.2 P-18ESect-12.2 P-19ESect-12.2 P-20ESect-12.2 P-21ESect-12.2 P-22ESect-12.2 P-23ESect-12.2 P-24ESect-12.2 P-25ESect-12.2 P-26ESect-12.2 P-27ESect-12.2 P-28ESect-12.2 P-29ESect-12.2 P-30ESect-12.2 P-31ESect-12.2 P-32ESect-12.2 P-33ESect-12.2 P-34ESect-12.2 P-35ESect-12.2 P-36ESect-12.2 P-37ESect-12.2 P-38ESect-12.2 P-39ESect-12.2 P-40ESect-12.2 P-41ESect-12.2 P-42ESect-12.2 P-43ESect-12.2 P-44ESect-12.2 P-45ESect-12.2 P-46ESect-12.2 P-47ESect-12.2 P-48ESect-12.2 P-49ESect-12.2 P-50ESect-12.2 P-51ESect-12.2 P-52ESect-12.3 P-1ESect-12.3 P-2ESect-12.3 P-3ESect-12.3 P-4ESect-12.3 P-5ESect-12.3 P-6ESect-12.3 P-7ESect-12.3 P-8ESect-12.3 P-9ESect-12.3 P-10ESect-12.3 P-11ESect-12.3 P-12ESect-12.3 P-13ESect-12.3 P-14ESect-12.3 P-15ESect-12.3 P-16ESect-12.3 P-17ESect-12.3 P-18ESect-12.3 P-19ESect-12.3 P-20ESect-12.3 P-21ESect-12.3 P-22ESect-12.3 P-23ESect-12.3 P-24ESect-12.3 P-25ESect-12.3 P-26ESect-12.3 P-27ESect-12.3 P-28ESect-12.3 P-29ESect-12.3 P-30ESect-12.3 P-31ESect-12.3 P-32ESect-12.3 P-33ESect-12.3 P-34ESect-12.3 P-35ESect-12.3 P-36ESect-12.3 P-37ESect-12.3 P-38ESect-12.3 P-39ESect-12.3 P-40ESect-12.3 P-41ESect-12.3 P-42ESect-12.3 P-43ESect-12.3 P-44ESect-12.3 P-45ESect-12.3 P-46ESect-12.3 P-47ESect-12.3 P-48ESect-12.3 P-49ESect-12.3 P-50ESect-12.3 P-51ESect-12.3 P-52ESect-12.3 P-53ESect-12.3 P-54ESect-12.3 P-55ESect-12.3 P-56ESect-12.3 P-57ESect-12.3 P-58ESect-12.3 P-59ESect-12.3 P-60ESect-12.3 P-61ESect-12.3 P-62ESect-12.3 P-63ESect-12.3 P-64ESect-12.3 P-65ESect-12.4 P-1ESect-12.4 P-2ESect-12.4 P-3ESect-12.4 P-4ESect-12.4 P-5ESect-12.4 P-6ESect-12.4 P-7ESect-12.4 P-8ESect-12.4 P-9ESect-12.4 P-10ESect-12.4 P-11ESect-12.4 P-12ESect-12.4 P-13ESect-12.4 P-14ESect-12.4 P-15ESect-12.4 P-16ESect-12.4 P-17ESect-12.4 P-18ESect-12.4 P-19ESect-12.4 P-20ESect-12.4 P-21ESect-12.4 P-22ESect-12.4 P-23ESect-12.4 P-24ESect-12.4 P-25ESect-12.4 P-26ESect-12.4 P-27ESect-12.4 P-28ESect-12.4 P-29ESect-12.4 P-30ESect-12.4 P-31ESect-12.4 P-32ESect-12.4 P-33ESect-12.4 P-34ESect-12.4 P-35ESect-12.4 P-36ESect-12.4 P-37ESect-12.4 P-38ESect-12.4 P-39ESect-12.4 P-40ESect-12.4 P-41ESect-12.4 P-42ESect-12.4 P-43ESect-12.4 P-44ESect-12.4 P-45ESect-12.4 P-47ESect-12.4 P-48ESect-12.4 P-49ESect-12.4 P-50ESect-12.4 P-51ESect-12.4 P-52ESect-12.4 P-53ESect-12.4 P-54ESect-12.5 P-1ESect-12.5 P-2ESect-12.5 P-3ESect-12.5 P-4ESect-12.5 P-5ESect-12.5 P-6ESect-12.5 P-7ESect-12.5 P-8ESect-12.5 P-9ESect-12.5 P-10ESect-12.5 P-11ESect-12.5 P-12ESect-12.5 P-13ESect-12.5 P-14ESect-12.5 P-15ESect-12.5 P-16ESect-12.5 P-17ESect-12.5 P-18ESect-12.5 P-19ESect-12.5 P-20ESect-12.5 P-21ESect-12.5 P-22ESect-12.5 P-23ESect-12.5 P-24ESect-12.5 P-25ESect-12.5 P-26ESect-12.5 P-27ESect-12.5 P-28ESect-12.5 P-29ESect-12.5 P-30ESect-12.5 P-31ESect-12.5 P-32ESect-12.5 P-33ESect-12.5 P-34ESect-12.5 P-35ESect-12.5 P-36ESect-12.5 P-37ESect-12.5 P-38ESect-12.5 P-39ESect-12.5 P-40ESect-12.5 P-41ESect-12.5 P-42ESect-12.5 P-43ESect-12.5 P-44ESect-12.5 P-45ESect-12.5 P-46ESect-12.5 P-47ESect-12.5 P-48ESect-12.5 P-49ESect-12.5 P-50ESect-12.5 P-51ESect-12.5 P-52ESect-12.5 P-53ESect-12.5 P-54ESect-12.5 P-55ESect-12.5 P-56ESect-12.5 P-57ESect-12.5 P-58ESect-12.5 P-59ESect-12.5 P-60ESect-12.5 P-61ESect-12.5 P-62ESect-12.5 P-63ESect-12.5 P-64ESect-12.5 P-65ESect-12.5 P-66ESect-12.5 P-67ESect-12.5 P-68ESect-12.5 P-69ESect-12.5 P-70ESect-12.5 P-71ESect-12.5 P-72ESect-12.5 P-73ESect-12.5 P-74ESect-12.5 P-75ESect-12.5 P-76ESect-12.5 P-77ESect-12.5 P-78ESect-12.5 P-79ESect-12.5 P-80ESect-12.5 P-81ESect-12.5 P-82ESect-12.5 P-83ESect-12.6 P-1ESect-12.6 P-2ESect-12.6 P-3ESect-12.6 P-4ESect-12.6 P-5ESect-12.6 P-6ESect-12.6 P-7ESect-12.6 P-8ESect-12.6 P-9ESect-12.6 P-10ESect-12.6 P-11ESect-12.6 P-12ESect-12.6 P-13ESect-12.6 P-14ESect-12.6 P-15ESect-12.6 P-16ESect-12.6 P-17ESect-12.6 P-18ESect-12.6 P-19ESect-12.6 P-20ESect-12.6 P-21ESect-12.6 P-22ESect-12.6 P-23ESect-12.6 P-24ESect-12.6 P-25ESect-12.6 P-26ESect-12.6 P-27ESect-12.6 P-28ESect-12.6 P-29ESect-12.6 P-30ESect-12.6 P-31ESect-12.6 P-32ESect-12.6 P-33ESect-12.6 P-34ESect-12.6 P-35ESect-12.6 P-36ESect-12.6 P-37ESect-12.6 P-38ESect-12.6 P-43ESect-12.6 P-44ESect-12.6 P-45ESect-12.6 P-46ESect-12.6 P-47ESect-12.6 P-48ESect-12.6 P-49ESect-12.6 P-50ESect-12.6 P-51ESect-12.6 P-52ECh-12 P-1RCCCh-12 P-2RCCCh-12 P-3RCCCh-12 P-4RCCCh-12 P-5RCCCh-12 P-6RCCCh-12 P-7RCCCh-12 P-8RCCCh-12 P-9RCCCh-12 P-10RCCCh-12 P-11RCCCh-12 P-12RCCCh-12 P-13RCCCh-12 P-14RCCCh-12 P-15RCCCh-12 P-16RCCCh-12 P-17RCCCh-12 P-18RCCCh-12 P-19RCCCh-12 P-1RQCh-12 P-2RQCh-12 P-3RQCh-12 P-4RQCh-12 P-5RQCh-12 P-6RQCh-12 P-7RQCh-12 P-8RQCh-12 P-9RQCh-12 P-10RQCh-12 P-11RQCh-12 P-12RQCh-12 P-13RQCh-12 P-14RQCh-12 P-15RQCh-12 P-16RQCh-12 P-17RQCh-12 P-18RQCh-12 P-19RQCh-12 P-20RQCh-12 P-21RQCh-12 P-22RQCh-12 P-1RECh-12 P-2RECh-12 P-3RECh-12 P-4RECh-12 P-5RECh-12 P-6RECh-12 P-7RECh-12 P-8RECh-12 P-9RECh-12 P-10RECh-12 P-11RECh-12 P-12RECh-12 P-13RECh-12 P-14RECh-12 P-15RECh-12 P-16RECh-12 P-17RECh-12 P-18RECh-12 P-19RECh-12 P-20RECh-12 P-21RECh-12 P-22RECh-12 P-23RECh-12 P-24RECh-12 P-25RECh-12 P-26RECh-12 P-27RECh-12 P-28RECh-12 P-29RECh-12 P-30RECh-12 P-31RECh-12 P-32RECh-12 P-33RECh-12 P-34RECh-12 P-35RECh-12 P-36RECh-12 P-37RECh-12 P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Find the general indefinite integral. (u62u5u3+27)du

Single Variable Calculus: Early Transcendentals, Volume I

A sample of n = 9 scores has X = 108. What is the sample mean?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Find the limit. limx1+x29x2+2x3

Calculus (MindTap Course List)

find the real roots of each equation by factoring. 129. x2 + x 12 = 0

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Perform the indicated operation for the following. 6.

Contemporary Mathematics for Business & Consumers

Use the following matrices for Problems 1-28. 20. .

Mathematical Applications for the Management, Life, and Social Sciences

Continuity In Exercises 61-66, discuss the continuity of the function. f(x,y,z)=xysinz

Calculus: Early Transcendental Functions (MindTap Course List)

True or False: The slope of a tangent line may be interpreted as average velocity.

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

The interval of convergence of is: [−1, 1] [−1, 1) (−1, 1] (−1, 1)

Study Guide for Stewart's Multivariable Calculus, 8th

Explain why control of extraneous variables is a critical component of an experiment.

Research Methods for the Behavioral Sciences (MindTap Course List)

Graph the solution set of each system. {x3y3x+3y3

College Algebra (MindTap Course List)