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

Use the formula in Exercise 42 to find the curvature.

44. x = a cos ωt, y = b sin ωt

To determine

To find: The curvature of the plane with parametric equations x=acosωt and y=bsinωt .

Explanation

Given data:

Parametric equations are x=acosωt and y=bsinωt .

Formula used:

The curvature of plane with parametric equation x=f(t) , y=g(t) is,

k(t)=|x˙y¨x¨y˙|(x˙2+y˙2)32 (1)

Here,

k(t) is curvature of the plane.

Consider the given equation.

x=acosωt

Differentiate the equation with respect to t.

x˙=ddt(acosωt)=addt(cosωt)=aωsinωt {ddx(cosax)=asinx}

Find the value of x¨ .

x¨=ddt(aωsinωt)=aω(ωcosωt) {ddx(sinax)=acosx}=aω2cosωt

Consider the given equation.

y=bsinωt

Differentiate the equation with respect to t.

y˙=ddt(bsinωt)=bddt(sinωt)=bωcosωt {ddx(sinax)=acosx}

Find the value of y¨ .

y¨=ddt(bωcosωt)=bω(ωsinωt) {ddx(cosax)=asinx}=bω2sinωt

Substitute aωsinωt for x˙ , aω2cosωt for x¨

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 13 Solutions

Show all chapter solutions add
Sect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.1 P-41ESect-13.1 P-42ESect-13.1 P-43ESect-13.1 P-44ESect-13.1 P-45ESect-13.1 P-46ESect-13.1 P-49ESect-13.1 P-50ESect-13.1 P-53ESect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 P-33ESect-13.2 P-34ESect-13.2 P-35ESect-13.2 P-36ESect-13.2 P-37ESect-13.2 P-38ESect-13.2 P-39ESect-13.2 P-40ESect-13.2 P-41ESect-13.2 P-42ESect-13.2 P-43ESect-13.2 P-44ESect-13.2 P-45ESect-13.2 P-46ESect-13.2 P-47ESect-13.2 P-48ESect-13.2 P-49ESect-13.2 P-50ESect-13.2 P-51ESect-13.2 P-52ESect-13.2 P-53ESect-13.2 P-54ESect-13.2 P-55ESect-13.2 P-56ESect-13.2 P-57ESect-13.2 P-58ESect-13.3 P-1ESect-13.3 P-2ESect-13.3 P-3ESect-13.3 P-4ESect-13.3 P-5ESect-13.3 P-6ESect-13.3 P-7ESect-13.3 P-8ESect-13.3 P-9ESect-13.3 P-10ESect-13.3 P-11ESect-13.3 P-12ESect-13.3 P-13ESect-13.3 P-14ESect-13.3 P-15ESect-13.3 P-16ESect-13.3 P-17ESect-13.3 P-18ESect-13.3 P-19ESect-13.3 P-20ESect-13.3 P-21ESect-13.3 P-22ESect-13.3 P-23ESect-13.3 P-24ESect-13.3 P-25ESect-13.3 P-26ESect-13.3 P-27ESect-13.3 P-28ESect-13.3 P-29ESect-13.3 P-30ESect-13.3 P-31ESect-13.3 P-32ESect-13.3 P-33ESect-13.3 P-38ESect-13.3 P-39ESect-13.3 P-42ESect-13.3 P-43ESect-13.3 P-44ESect-13.3 P-45ESect-13.3 P-46ESect-13.3 P-47ESect-13.3 P-48ESect-13.3 P-49ESect-13.3 P-50ESect-13.3 P-53ESect-13.3 P-55ESect-13.3 P-56ESect-13.3 P-58ESect-13.3 P-59ESect-13.3 P-60ESect-13.3 P-62ESect-13.3 P-63ESect-13.3 P-64ESect-13.3 P-65ESect-13.3 P-66ESect-13.3 P-67ESect-13.4 P-1ESect-13.4 P-3ESect-13.4 P-4ESect-13.4 P-5ESect-13.4 P-6ESect-13.4 P-7ESect-13.4 P-8ESect-13.4 P-9ESect-13.4 P-10ESect-13.4 P-11ESect-13.4 P-12ESect-13.4 P-13ESect-13.4 P-14ESect-13.4 P-15ESect-13.4 P-16ESect-13.4 P-19ESect-13.4 P-20ESect-13.4 P-21ESect-13.4 P-22ESect-13.4 P-23ESect-13.4 P-24ESect-13.4 P-25ESect-13.4 P-26ESect-13.4 P-27ESect-13.4 P-28ESect-13.4 P-29ESect-13.4 P-30ESect-13.4 P-31ESect-13.4 P-32ESect-13.4 P-34ESect-13.4 P-35ESect-13.4 P-36ESect-13.4 P-37ESect-13.4 P-38ESect-13.4 P-39ESect-13.4 P-40ESect-13.4 P-41ESect-13.4 P-42ESect-13.4 P-44ESect-13.4 P-45ESect-13.4 P-46ECh-13 P-1RCCCh-13 P-2RCCCh-13 P-3RCCCh-13 P-4RCCCh-13 P-5RCCCh-13 P-6RCCCh-13 P-7RCCCh-13 P-8RCCCh-13 P-9RCCCh-13 P-1RQCh-13 P-2RQCh-13 P-3RQCh-13 P-4RQCh-13 P-5RQCh-13 P-6RQCh-13 P-7RQCh-13 P-8RQCh-13 P-9RQCh-13 P-10RQCh-13 P-11RQCh-13 P-12RQCh-13 P-13RQCh-13 P-14RQCh-13 P-1RECh-13 P-2RECh-13 P-3RECh-13 P-4RECh-13 P-5RECh-13 P-6RECh-13 P-7RECh-13 P-8RECh-13 P-9RECh-13 P-10RECh-13 P-11RECh-13 P-12RECh-13 P-13RECh-13 P-14RECh-13 P-15RECh-13 P-16RECh-13 P-17RECh-13 P-18RECh-13 P-19RECh-13 P-20RECh-13 P-21RECh-13 P-22RECh-13 P-23RECh-13 P-1PCh-13 P-2PCh-13 P-3PCh-13 P-4PCh-13 P-5PCh-13 P-6PCh-13 P-7PCh-13 P-8PCh-13 P-9P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Differentiate the function. f(t) = 2t3 3t2 4t

Calculus: Early Transcendentals

Solve the inequality. 55. 1 |x| 4

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 4756, solve the given equation for the indicated variable. 5x+1=1125

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 1520, simplify the expression. 17. 16x5yz481xyz54; x 0, y 0, z 0

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

Find the limit. limx3x29x2+2x3

Single Variable Calculus: Early Transcendentals

True or False:

Study Guide for Stewart's Multivariable Calculus, 8th

Sometimes, Always, or Never: If {an} is increasing and bounded above, then {an} converges.

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