menu
bartleby
search
close search
Hit Return to see all results
Subscribe
Sign in
Subjects
Business
Accounting
Economics
Finance
Leadership
Management
Marketing
Operations Management
Engineering
Bioengineering
Chemical Engineering
Civil Engineering
Computer Engineering
Computer Science
Electrical Engineering
Mechanical Engineering
Math
Advanced Math
Algebra
Calculus
Geometry
Probability
Statistics
Trigonometry
Science
Advanced Physics
Biochemistry
Biology
Chemistry
Earth Science
Health & Nutrition
Nursing
Physics
Social Science
Anthropology
Psychology
Sociology

Math
CalculusMultivariable Calculus8th Edition

close solutoin list
Chapter 13.3, Problem 65E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 38E
Problem 39E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 53E
Problem 55E
Problem 56E
Problem 58E
Problem 59E
Problem 60E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Use the formula in Exercise 63(d) to find the torsion of the curve r ( t ) = 〈 t , 1 2 t 2 , 1 3 t 3 〉 .

To determine

To find: The torsion of the curve r(t)=〈t,12t2,13t3〉 .

Explanation

Formula:

Write the expression for torsion of curve r(t) .

τ=(r′(t)×r″(t))⋅r‴(t)|r′(t)×r″(t)|2 (1)

Here,

r′(t) is first derivative of r(t) ,

r″(t) is second derivative of r(t) , and

r‴(t) is third derivative of r(t) ,

Consider the two three-dimensional vector functions such as u(t)=〈u1(t),u2(t),u3(t)〉 and v(t)=〈v1(t),v2(t),v3(t)〉 .

Cross product of vectors:

Write the expression for cross product of vectors u(t) and v(t) (u(t)×v(t)) .

u(t)×v(t)=|ijku1(t)u2(t)u3(t)v1(t)v2(t)v3(t)|=〈[(u2(t)v3(t)−v2(t)u3(t))],[−(u1(t)v3(t)−v1(t)u3(t))],[(u1(t)v2(t)−v1(t)u2(t))]〉

Dot product of vectors:

Write the expression for dot product of vectors u(t) and v(t) (u(t)â‹…v(t)) .

u(t)⋅v(t)=〈u1(t),u2(t),u3(t)〉⋅〈v1(t),v2(t),v3(t)〉=u1(t)v1(t)+u2(t)v2(t)+u3(t)v3(t)

Find the value of r′(t) .

r′(t)=ddt〈t,12t2,13t3〉=〈ddt(t),ddt(12t2),ddt(13t3)〉=〈1,12(2t),13(3t2)〉                        {∵ddx(xn)=nxn−1}=〈1,t,t2〉

Apply differentiation with respect to t on both sides of equation.

r″(t)=ddt〈1,t,t2〉=〈ddt(1),ddt(t),ddt(t2)〉=〈0,1,2t〉                        {∵ddx(k)=0,ddx(x)=1,ddx(xn)=nxn−1}

Apply differentiation with respect to t on both sides of equation

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 13.3,
Problem 64E
Chapter 13.3,
Problem 66E
arrow_forward

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-1ESect-13.1 P-2ESect-13.1 P-3ESect-13.1 P-4ESect-13.1 P-5ESect-13.1 P-6ESect-13.1 P-7ESect-13.1 P-8ESect-13.1 P-9ESect-13.1 P-10E
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

Finding a for a Given In Exercises 41-46, Find the limit L. Then Find such that |f(x)L| whenever 0|xc| for (...

Calculus: Early Transcendental Functions

Inequalities Involving Quotients Solve the nonlinear inequality. Express the solution using interval notation, ...

Precalculus: Mathematics for Calculus (Standalone Book)

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the integral. 11. 1x3x21dx

Calculus: Early Transcendentals

Sketch the region in the xy-plane. 45. {(x, y) | xy 0}

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 13, (a) find the distance between the points, (b) find the midpoint of the line segment joining th...

Calculus: An Applied Approach (MindTap Course List)

Simplify the expressions in Exercises 5764, given that x,y,z,a,b, and c are positive real numbers. 4(x2+y2)c2

Applied Calculus

SOC/CJ Statewide, the police clear by arrest 35 of the robberies and 42 of the aggravated assaults reported to ...

Essentials Of Statistics

A research study comparing alcohol use for college students in the United States and Canada reports that more C...

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

8-68 Find the limit. Use IHospitals Rule where appropriate. If there is a more elementary method, consider usin...

Calculus (MindTap Course List)

The spotlight effect refers to overestimating the extent to which others notice your appearance or behaviour, e...

Statistics for The Behavioral Sciences (MindTap Course List)

For Problems 15-20, use the specified number of classes to do the following. (a) Find the class width. (b) Make...

Understanding Basic Statistics

In Exercises 39-54, simplify the expression. (Assume that x, y, r, s, and t are positive.) 43. x3/4x1/4

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

Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. 50. 2 si...

Single Variable Calculus

Solve the system { 3x+2y=24x+5y=2

Mathematical Applications for the Management, Life, and Social Sciences

By any method, determine all possible real solutions of each equation in Exercises 1330. Check your answers by ...

Finite Mathematics

Suppose that you read through this years issues of the New York Times and record each number that appears in a ...

Probability and Statistics for Engineering and the Sciences

For Problems 64-78, translate each English phrase into an algebraic expression and use n to represent the unkno...

Intermediate Algebra

For Questions 5 and 6, assume triangle ABC has sides a, b, and c. State the formula for the semi perimeter of t...

Trigonometry (MindTap Course List)

Given: mDOE=76and mEOG=82inO EFisadiameter Find: a mDE b mDF c mF d mDGE e mEHG f WhethermEHG=12(mEG+mDF)

Elementary Geometry For College Students, 7e

Find a. the tolerance in ohms, b. the upper limit, c. the lower limit, and d. the tolerance interval for each ...

Elementary Technical Mathematics

For the following second mortgage applications, calculate the percentage of appraised value and the potential c...

Contemporary Mathematics for Business & Consumers

Prove or disprove that the polynomial can be factored as the product of two polynomials of degree in where ...

Elements Of Modern Algebra

In Exercises 5 and 6, use set-builder notation to write each of the given sets. 5. {0,1,2,3,4,5, 6} 6. {-3, -2,...

Mathematical Excursions (MindTap Course List)

Identifying and Sketching a Conic In Exercises 13-22, find the eccentricity and the distance from the pole to t...

Calculus: Early Transcendental Functions (MindTap Course List)

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Single Variable Calculus: Early Transcendentals

Finding an Indefinite Integral In Exercises 9-30, find the indefinite integral and check the result by differen...

Calculus of a Single Variable

Construct an angle that measures 75.

Elementary Geometry for College Students

In Exercises 14, find an equation of the least-squares line for the data. x -2.1 -1.1 0.1 1.4 2.6 4.2 5.1 y 6.2...

Finite Mathematics for the Managerial, Life, and Social Sciences

A bacteria population grows in such a way that after t hours its population is 1000 + 10t + t3. The growth rate...

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

Finding a General Solution In exercises 19-28, find the general solution of the linear differential equation. y...

Multivariable Calculus

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

Calculus

True or False: If the vector c is orthogonal to both vectors a and b, then c is a scalar multiple of a × b.

Study Guide for Stewart's Multivariable Calculus, 8th

Self Check Expand: (pq)3.

College Algebra (MindTap Course List)

Express each percent as a decimal fraction or mixed decimal. 36. 103%

Mathematics For Machine Technology

Return to Exercise 6.118, and suppose that 4 bulbs are randomly selected from the 25. a. What is the probabilit...

Introduction To Statistics And Data Analysis

Area In Exercises 2932, use a line integral to find the area of the region R R: Region inside the loop of the f...

Calculus (MindTap Course List)

Define the three types of survey questions (open ended, restricted, and rating-scale) and identify the relative...

Research Methods for the Behavioral Sciences (MindTap Course List)

Registered nurses in 2007 made an average hourly wage of 30.04. In 2011, their hourly wage had risen to 33.23. ...

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

Identify the characteristics that differentiate different sets of data and identify the hypothesis test(s) appr...

Research Methods for the Behavioral Sciences (MindTap Course List)

Nielsen Research provides weekly ratings of nationally broadcast television programs. The ratings of the 84 pri...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

bartleby
© bartleby 2019