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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 3.10, Problem 21E
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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 41E
Problem 42E
Problem 43E
Problem 44E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Compute ∆y and dy for the given values of x and dx = ∆x. Then sketch a diagram like Figure 5 showing the line segments with lengths dx, dy, and ∆y.

21. y = x − 2 ,   x = 3 ,   Δ x = 0.8

To determine

To compute: The value Δy and dy for the given values of x and dx=Δx. Sketch the line segment with lengths dy,Δy and dx.

Explanation

Given:

The function is y=x−2. The value x=3 and Δx=0.8

Calculation:

Obtain the value of Δy.

Consider the function f(x)=x−2.

Δy=f(x+Δx)−f(x)

Substitute the value x=3 and Δx=0.8,

Δy=f(3+0.8)−f(3)=f(3.8)−f(3)=3.8−2−3−2=1.8−1

Simplify the terms,

Δy=1.341−1=0.341≈0.34

Thus, the value Δy≈0.34.

Obtain the value of dy.

Note that, the differential is dy=f′(x)dx.

The derivative of the function f(x) is computed as follows,

f′(x)=ddx(x−2)=12(x−2)12−1

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Chapter 3.10,
Problem 20E
Chapter 3.10,
Problem 22E
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Finding the Slope of a Graph In Exercises 37-44, find the slope of the graph of the function at the given point...

Calculus: An Applied Approach (MindTap Course List)

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Think About It Use a graphing utility to graph f(x)=sin x and g(x)=arcsin(sinx). Is the graph of g the line y=x...

Calculus: Early Transcendental Functions

Radical Expressions Evaluate the radical expression, and express the result in the form a + bi. 55. 312

Precalculus: Mathematics for Calculus (Standalone Book)

A sample of n = 5 scores has a mean of M = 12. If one new score with a value of X 18 is added to the sample, t...

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

Exercises You can use the following problems as a self-test on the material presented in this review. If you ca...

Essentials Of Statistics

Given the equation 2x + 3y = 4, answer the following questions: a. Is the slope of the line described by this e...

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

Test the series for convergence or divergence. n=21nlnn

Calculus (MindTap Course List)

Sketch the graph of a function f that is continuous except for the stated discontinuity. 8. Neither left nor ri...

Single Variable Calculus

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Finite Mathematics

Expand Your knowledge: Split Stem The Boston Marathon is the oldest and best-known U.S. marathon. It covers a r...

Understanding Basic Statistics

An example of the vertical-horizontal illusion is shown in the figure. Although the two lines are exactly the s...

Statistics for The Behavioral Sciences (MindTap Course List)

In problems 24-26, find the intercepts and graph. 25.

Mathematical Applications for the Management, Life, and Social Sciences

For Problems 1-50, solve each equation. Objective 1 3(4n+2)+2(n6)=2(n+1)

Intermediate Algebra

Problems from the Mensa Workout Mensa is a society that welcomes people from every walk of life whose IQ is in ...

Mathematical Excursions (MindTap Course List)

Let X1,..., Xn be a random sample from a gamma distribution with parameters and . a. Derive the equations whos...

Probability and Statistics for Engineering and the Sciences

(a) Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and...

Single Variable Calculus: Early Transcendentals

Find the amount of interest and the maturity value of the following loans. Use the formula MV = P + I to find t...

Contemporary Mathematics for Business & Consumers

Suppose G1 and G2 are groups with normal subgroups H1 and H2, respectively, and with G1/H1 isomorphic to G2/H2....

Elements Of Modern Algebra

Read the measurement in inches shown on each vernier caliper:

Elementary Technical Mathematics

Find all degree solutions. 2cos22cos21=0

Trigonometry (MindTap Course List)

For the drawing in Exercise 44, suppose that the larger gear has 20 teeth and the smaller gear has 10 the gear ...

Elementary Geometry For College Students, 7e

Matching In Exercises 49-52, match the logistic equation with its graph. [The graphs are labeled (a), (b), (c),...

Calculus of a Single Variable

Using the Fundamental Theorem of line Integrals In Exercises 47-50, evaluate CF.dr using the Fundamental Theore...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 35 and 36, complete each proof using the drawing below. Given:ABAC Prove:67 PROOF Statements Reaso...

Elementary Geometry for College Students

GUN OWNERS IN THE HOUSE OF REPRESENTATIVES As of January 3,2013, the U.S. House of Representatives was made up ...

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False? In Exercises 83-86, determine whether the statement is true or false. If it is false, explain wh...

Calculus

Sketching a Vector In Exercises 87 und 88, sketch the vector v and write its component form. v lies in the xz-p...

Calculus (MindTap Course List)

True or False If the series converges to a number s, then all rearrangements of also converge to s.

Study Guide for Stewart's Multivariable Calculus, 8th

EXPLORING CONCEPTS Think About ItIn Exercises 57 and 58, consider two forces of equal magnitude acting on a poi...

Multivariable Calculus

True or False: y = xex is a solution to y=y+yx.

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

A researcher conducting a political poll for a statewide election would like to know the attitudes of college s...

Research Methods for the Behavioral Sciences (MindTap Course List)

A sample of 9 days over the past six months showed that a dentist treated the following numbers of patients: 22...

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

Express the following decimal numbers as binary numbers. 14

Mathematics For Machine Technology

Decompose each fraction into partial fractions. 2x4+6x3+20x2+22x+25xx2+2x+52

College Algebra (MindTap Course List)

Describe how time-related factors such as history, maturation, instrumentation, statistical regression, and ord...

Research Methods for the Behavioral Sciences (MindTap Course List)

A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is = 5. ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Students in a representative sample of 65 first-year students selected from a large university in England parti...

Introduction To Statistics And Data Analysis

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