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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.4, Problem 92E
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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
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 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Problem 84E
Problem 85E
Problem 86E
Problem 87E
Problem 88E
Problem 89E
Problem 90E
Problem 91E
Problem 92E
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Let

f ( x ) = { | x | x if   x ≠ 0 1 if   x = 0

(a) Show that f is continuous at 0.

(b) Investigate graphically whether f is differentiable at 0 by zooming in several limes toward the point (0, 1) on the graph of f.

(c) Show that f is not differentiable at 0. How can you reconcile this fact with the appearance of the graphs in part (b)?

(a)

To determine

To show: The function f is continuous at 0 if f(x)={|x|xif x≠01if x=0 .

Explanation

Proof:

To show that f is continuous at 0 it is sufficient to show that limx→0f(x)=f(0) that is limx→0f(x)=1 .

Let y=limx→0|x|x . (1)

Take natural logarithm on both sides,

lny=ln(y=limx→0|x|x)=limx→0(ln|x|x)=limx→0(xln|x|)=limx→0ln|x|1x

Therefore, lny=limx→0ln|x|1x . (2)

Obtain the value of the function as x approaches 0 .

As x approaches 0 , the numerator is,

ln|x|=ln|0|=∞

As x approaches 0 , the denominator is, 1x=∞

(b)

To determine

To check: Whether the function f(x)={|x|xif x≠01if x=0 is differentiable at 0 by zooming the graph towards the point (0,1) .

(c)

To determine

To show: The function f(x)={|x|xif x≠01if x=0 is not differentiable at 0; explain how it contradicts with the graphs appeared in the part (b).

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For a population with a mean of =40 and a standard deviation of =8 , find the z-score corresponding to each of ...

Statistics for The Behavioral Sciences (MindTap Course List)

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

In Exercises 29 to 36, draw a Venn diagram to show each of the following sets. (AB)B

Mathematical Excursions (MindTap Course List)

Thoughts Into Words For what natural numbers n does (1)n=1? For what natural numbers n does (1)n=1? Explain you...

Intermediate Algebra

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. 2x3x2...

Finite Mathematics

Example 4.5 introduced the concept of time headway in traffic flow and proposed a particular distribution for X...

Probability and Statistics for Engineering and the Sciences

In Problems 7-34, perform the indicated operations and simplify. 15.

Mathematical Applications for the Management, Life, and Social Sciences

Show that the equation has exactly one real root. 2x + cos x = 0

Single Variable Calculus: Early Transcendentals

Label each of the following statements as either true or false. Let g:AB and f:BC such that fg is one-to-one. T...

Elements Of Modern Algebra

Find all solutions in radians using exact values only. sin3xcos2x+cos3xsin2x=1

Trigonometry (MindTap Course List)

In Exercises 29 to 34, use the Law of Sines or the Law of Cosines to solve each problem. Angle measures should ...

Elementary Geometry For College Students, 7e

Perform the indicated operation: 4x2(82x+3x2)

Elementary Technical Mathematics

45. An insurance adjuster for UPS found that 12% of a shipment was damaged in transit. If the damaged goods amo...

Contemporary Mathematics for Business & Consumers

Changing the Order of Integration In Exercises 61-66, sketch the region of integration. Then evaluate the itera...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding a Derivative In Exercises 65-74, find the derivative of the function. y=cosh1(3x)

Calculus of a Single Variable

In Exercises 35 and 36, use Theorem 2.5.1 to solve the problem. According to this theorem, the number of diagon...

Elementary Geometry for College Students

In Exercises 2932, a fair die is dolled, and the number that falls uppermost is observed. Let E and F be events...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding a Particular Solution In Exercises17-22, find the particular solution of the differentialequation that ...

Multivariable Calculus

True or False: a × b is a vector in the plane formed by vectors a and b.

Study Guide for Stewart's Multivariable Calculus, 8th

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

Calculus

True or False: If Tn(x) is the nth Taylor polynomial for f(x) centered at c, then Tn(k)(c) = f(k)(c) for k = 0,...

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

Solve each of the following equations using either the multiplication, root, or power principal of equality. Ch...

Mathematics For Machine Technology

Allegiant Airlines charges a mean base fare of 89. In addition, the airline charges for making a reservation on...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The article Zoning and Industrial Land Values: The Case of Philadelphia (AREUEA Journal [1991]: 154159) conside...

Introduction To Statistics And Data Analysis

Define a positive relationship and a negative relationship and explain the how consistency of positive and nega...

Research Methods for the Behavioral Sciences (MindTap Course List)

What is the general purpose of a manipulation check?

Research Methods for the Behavioral Sciences (MindTap Course List)

An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 ...

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

Critical Thinking Determine if the statement is true or false. If the statement is false, then correct it and m...

College Algebra (MindTap Course List)

Finding Intercepts In Exercises 1-4, find any intercepts. y=x3x4

Calculus (MindTap Course List)

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