menu
bartleby
search
close search
Hit Return to see all results
Subscribe
Sign in

Math
CalculusMultivariable Calculus8th Edition

close solutoin list
Chapter 13.2, Problem 50E
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 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

If r(t) = u(t) × v(t), where u and v are the vector functions in Exercise 49, find r'(2).

To determine

To find: The vector r′(2) .

Explanation

Given:

r(t)=u(t)×v(t) , u(2)=〈1, 2, −1〉 , u′(2)=〈3, 0, 4〉 , and v(t)=〈t, t2, t3〉 .

Formula used:

Write the expression to find the derivative of cross product of the two vectors u(t) and v(t) .

ddt[u(t)×v(t)]=u′(t)×v(t)+u(t)×v′(t) (1)

The vector r′(2) is the derivative of the vector function r(t)=u(t)×v(t) at t=2 .

Write the vector function r(t) as follows.

r(t)=u(t)×v(t)

Differentiate on both sides of the expression with respect to t .

ddt[r(t)]=ddt[u(t)×v(t)]

Rewrite the expression as follows.

r′(t)=ddt[u(t)×v(t)]

Substitute 2 for t,

r′(2)=ddt[u(2)×v(2)] (2)

Use the formula in equation (1) and rewrite the expression in equation (2) as follows.

r′(2)=u′(2)×v(2)+u(2)×v′(2) (3)

Calculation of vector v(2) :

Substitute 2 for t in the expression v(t)=〈t, t2, t3〉 ,

v(2)=〈2, 22, 23〉=〈2, 4, 8〉

Calculation of vector v′(t) :

The vector v′(t) is the derivative of the vector function v(t)=〈t, t2, t3〉 .

Differentiate each component of the vector function v(t)=〈t, t2, t3〉 to obtain the vector v′(t) as follows.

ddt[v(t)]=ddt〈t, t2, t3〉

v′(t)=〈ddt(t), ddt(t2), ddt(t3)〉

Use the following formula and compute the expression.

ddttn=ntn−1

Compute the expression v′(t)=〈ddt(t), ddt(t2), ddt(t3)〉 as follows.

v′(t)=〈1, 2t, 3t2〉

Calculation of vector v′(2) :

Substitute 2 for t in the expression,

v′(2)=〈1, 2(2), 3(22)〉=〈1, 4, 12〉

Calculation u′(2)×v(2) :

Substitute 〈3, 0, 4〉 for u′(2) and 〈2, 4, 8〉 for v(2) in the expression u′(2)×v(2) ,

u′(2)×v(2)=〈3, 0, 4〉×〈2, 4, 8〉

Rewrite and compute the expression as follows

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 13.2,
Problem 49E
Chapter 13.2,
Problem 51E
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

Find an equation of the tangent line to the curve at the given point. y = 4x 3x2, (2, 4)

Calculus: Early Transcendentals

In Exercises 7-10, evaluate the expression for the given value of x. ExpressionxValuey=5xx=2

Calculus: An Applied Approach (MindTap Course List)

Purchases OHaganBooks.com has been promoting a number of books published by Duffin House. The following table s...

Applied Calculus

Evaluate the integral, if it exists. 01ex1+e2xdx

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Deciding Whether an Equation In Exercises whether is a function In Exercises 43-46, determine whether y is a fu...

Calculus: Early Transcendental Functions

Linear Equations The given equation is either linear or equivalent to a linear equation. Solve the equation. 23...

Precalculus: Mathematics for Calculus (Standalone Book)

Stephens, Atkins, and Kingston (2009) conducted an experiment in which participants were able to tolerate more ...

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

SOC A researcher is studying changes in the student body at her university and has selected a random sample of ...

Essentials Of Statistics

Evaluate the difference quotient for the given function. Simplify your answer. f(x)=1x, f(x)f(a)xa

Calculus (MindTap Course List)

Gaucher, Friesen, and Kay (2010) found that masculine-themed words (such as competitive, independent, analyze, ...

Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 9-16, complete the table by computing f(x) at the given values of x. Use these results to estimate...

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

Prove the statement using the , definition of a limit. 29. limx2(x24x+5)=1

Single Variable Calculus

A college library has five copies of a certain text on reserve. Two copies (1 and 2) are first printings, and t...

Probability and Statistics for Engineering and the Sciences

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

Finite Mathematics

Statistical Literacy Marcie conducted a study of the cost of breakfast cereal. She recorded the costs of severa...

Understanding Basic Statistics

Determine whether the argument is an example of inductive reasoning or deductive reasoning. All books written b...

Mathematical Excursions (MindTap Course List)

In problems 9-18, simplify the expressions with all exponents positive. 18.

Mathematical Applications for the Management, Life, and Social Sciences

Find the measurement that is a. the least accurate and b. the least precise: 0.0005A;0.0060A;0.425A;0.0105A;0.0...

Elementary Technical Mathematics

Simplify each expression by using the Quotient Property of Square Roots: a 14 c 536 b 169 d 316

Elementary Geometry For College Students, 7e

For Problems 11-18, from the list 0,14,23,,7,1114,2.34,19,558,17,3.21,and2.6, identify each of the following. O...

Intermediate Algebra

Convert the following percents to reduced fractions, mixed numbers, or whole numbers. 23. 89%

Contemporary Mathematics for Business & Consumers

Finding the Mass of a Lamina In exercises 3-6, find the mass of the lamina described by the inequalities given ...

Calculus: Early Transcendental Functions (MindTap Course List)

The region under the curve y = sin2.x from 0 to is rotated about the x-axis. Find the volume of the resulting ...

Single Variable Calculus: Early Transcendentals

Graphical, Numerical, and Analytic Analysis In Exercises 75-82, use a graphing utility to graph the function an...

Calculus of a Single Variable

Label each of the following statements as either true or false. If p(x) is an irreducible polynomial over a fie...

Elements Of Modern Algebra

Use half-angle formulas to find the exact values for each of the following. tan165

Trigonometry (MindTap Course List)

The dye dilution method is used to measure the cardiac output of a pig’s heart with 10 mg of dye. After t secon...

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

Rectangular coordinates of the point with polar coordinates are: (−1, 0) (0, 1) (0, −1) (1, 0)

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 1926, pivot the system about the circled element. [2431|82]

Finite Mathematics for the Managerial, Life, and Social Sciences

In the figure for Exercises 21 to 24,RS is tangent to the circle at S. See Theorem 6.3.7. Given: RT=12RSandTV=9...

Elementary Geometry for College Students

Finding the Slope of a Tangent Line In Exercises 9-14, find the slope of the tangent line to the graph of the f...

Calculus (MindTap Course List)

Deciding Whether an Equation is a Function In Exercises 49 and 50, determine whether y is a function of x. x=9y...

Calculus

Kepler's Laws In Exercises 87-94, you are asked to verify Kepler's Laws of Planetary Motion. For these exercise...

Multivariable Calculus

Last year, 46% of business owners gave a holiday gift to their employees. A survey ofbusiness owners conducted ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain how a factorial study can combine different research designs (between and within subjects) and differen...

Research Methods for the Behavioral Sciences (MindTap Course List)

Is ultrasound a reliable method for determining the gender of an unborn baby? The accompanying data on 1000 bir...

Introduction To Statistics And Data Analysis

Substitute the given numbers for letters and find the values of the following expressions. If a=5 and c=3 , fin...

Mathematics For Machine Technology

During early 2012, economic hardship was stretching the limits of Frances welfaresystem. One indicator of the l...

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

Define plagiarism and explain the techniques that can be used to help avoid unintentional plagiarism.

Research Methods for the Behavioral Sciences (MindTap Course List)

Write an equation in standard form of each hyperbola described. Focus (4,0); vertex (2,0); center (0,0) .

College Algebra (MindTap Course List)

bartleby
© bartleby 2019