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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 3.5, Problem 75E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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 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
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find all points on the curve x2y2 + xy = 2 where the slope of the tangent line is –1.

To determine

To find: The points at which the slope of the curve is -1.

Explanation

Given:

The curve x2y2+xy=2.

Derivative rules:

Product rule: ddx(fg)=fddu(g)+gddx(f)

Chain rule: dydx=dydu⋅dudx

Calculation:

Differentiate x2y2+xy=2 implicitly with respect to x,

ddx(x2y2+xy)=ddx(2)ddx(x2y2)+ddx(xy)=0

Apply the product rule,

[x2ddx(y2)+y2ddx(x2)]+[xddx(y)+yddx(x)]=0[x2ddx(y2)+y2(2x)]+[xdydx+y(1)]=0

Apply the chain rule and simplify the terms,

x2ddy(y2)dydx+2xy2+xdydx+y=0(2x2y+x)dydx+2xy2+y=0(2x2y+x)dydx=−2xy2−ydydx=−2xy2−y2x2y+x

Thus, the derivative of the equation is dydx=−2xy2−y2x2y+x.

That is, the slope of the tangent is dydx=−2xy2−y2x2y+x

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Chapter 3.5,
Problem 74E
Chapter 3.5,
Problem 76E
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Sect-3.1 P-1ESect-3.1 P-2ESect-3.1 P-3ESect-3.1 P-4ESect-3.1 P-5ESect-3.1 P-6ESect-3.1 P-7ESect-3.1 P-8ESect-3.1 P-9ESect-3.1 P-10E
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Suppose f is a continuous positive decreasing function for x 1 and an = f(n). By drawing a picture, rank the f...

Multivariable Calculus

Evaluate expressions in Exercises 3756, rounding your answer to four significant digits where necessary. 169

Applied Calculus

Supply and Demand The demand and supply equations for an MP3 player are given by p=19015xDemandequationp=75+8xS...

Calculus: An Applied Approach (MindTap Course List)

Testing Whether a Function Is One-to-One In Exercises 49-54, determine whether the function is one-to-one. If i...

Calculus: Early Transcendental Functions

Sketch the graphs of the equations in Exercises 512. x2y=1

Finite Mathematics and Applied Calculus (MindTap Course List)

SOC The survey mentioned in problem 6.5 found that 25 of the 178 households consisted of unmarried couples who ...

Essentials Of Statistics

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Match the vector fields F on 3 with the plots labelled IIV. Give reasons for your choices. F(x,y,z)=xi+yj+zk

Calculus (MindTap Course List)

In Exercises 3540, rationalize the numerator of each expression. 35. x3

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

Simulation: Birthday Problem Suppose there are 30 people at a party. Do you think any two share the same birthd...

Understanding Basic Statistics

Briefly explain how increasing sample size influences each of the following. Assume that all other factors are ...

Statistics for The Behavioral Sciences (MindTap Course List)

What does the Squeeze Theorem say?

Single Variable Calculus

Sketch the graphs of the equations in Exercises 512. x2y=1

Finite Mathematics

In problems 23-58, perform the indicated operations and simplify. 28.

Mathematical Applications for the Management, Life, and Social Sciences

Find a Sum Find the following sum without using a calculator. 1+2+3+4+...+497+498+499+500

Mathematical Excursions (MindTap Course List)

Consider the pdf for total waiting time Y for two buses f(y)={125y0y1025125y5y100otherwise introduced in Exerci...

Probability and Statistics for Engineering and the Sciences

For Problems 79-99, answer the question with an algebraic expression. Objective 3 The sum of two numbers is 65,...

Intermediate Algebra

Find the most general antiderivative of the function. f(x) = x3 + cosh x

Single Variable Calculus: Early Transcendentals

Prove that z1z2zn=z1z2zn for complex numbers z1,z2,,zn..

Elements Of Modern Algebra

22. You are a real estate broker for Aurora Realty. One of your clients. Erica Heston, has agreed to purchase o...

Contemporary Mathematics for Business & Consumers

Show that each of the following statements is an identity by transforming the left side of each one into the ri...

Trigonometry (MindTap Course List)

In Exercise 29 to 37, angle measures should be given to the nearest degree; distances should be given to the ne...

Elementary Geometry For College Students, 7e

Add the following signed number: (7)+(+8)

Elementary Technical Mathematics

Determining a Differentiable Function In Exercises 47 and 48, find dy / dx implicitly and find the largest inte...

Calculus of a Single Variable

Sketching a Surface in Space In Exercises11-14, describe and sketch the surface. y2+z2=9

Calculus: Early Transcendental Functions (MindTap Course List)

Assume that the probability of a boy being born is the same as the probability of a girl being born. In Exercis...

Finite Mathematics for the Managerial, Life, and Social Sciences

Use Theorem 11.4.1 to show that the area of an equilateral triangle with sides of length s is given by A=s243.

Elementary Geometry for College Students

Finding the Standard Equation of a Hyperbola In Exercises 41-48, find the standard form of the equation of the ...

Calculus

True or False: div curl F = 0.

Study Guide for Stewart's Multivariable Calculus, 8th

Finding a Trigonometric Integral In Exercises 1726, find the trigonometric integral. (cos)(sin+cos)2d

Calculus (MindTap Course List)

Surface Area Consider the surface f(x,y)=x+y. What is the relationship between the area of the surface that lie...

Multivariable Calculus

The graph of is: a) b) c) d)

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

Briefly explain how an order effect such as fatigue can be a confounding variable in a within-subjects design.

Research Methods for the Behavioral Sciences (MindTap Course List)

In exercise 2, 10 observations were provided for a dependent variable 5 and two independent variables x1 and x2...

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

A special industrial battery must have a life of at least 400 hours. A hypothesis test is tobe conducted with a...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In Exercises 2128, express the given biconditionals as the conjunction of two conditionals. You obtain a refund...

Mathematics: A Practical Odyssey

Briefly explain how a participant characteristic, such as personality, could be a confounding variable in a bet...

Research Methods for the Behavioral Sciences (MindTap Course List)

Applications Use a calculator to help solve each problem. Saving for retirement When Grayson was 20 years old, ...

College Algebra (MindTap Course List)

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal...

Mathematics For Machine Technology

The graph in the figure at the top of the following page appeared in the report Testing the Waters 2009 (Natura...

Introduction To Statistics And Data Analysis

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