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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.4, Problem 47E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

A function f is a ratio of quadratic functions and has a vertical asymptote x = 4 and just one x-intercept, x = 1 .It is known that f has a removable discontinuity at x = − 1 and lim x →   − 1 f ( x ) = 2 Evaluate

(a) f ( 0 )

(b) lim x →   ∞ f ( x )

(a)

To determine

To evaluate:

The value of f(0)

Explanation

1) Concept:

From the given information, construct a function and evaluate the function at x=0

2) Calculation:

f is a rational function and has vertical asymptote at x=4

This shows (x-4) is one of the factors of denominator

x=1is x- intercept which shows (x-1) is one of the factor of numerator

Now, f has a removable discontinuity at x=-1

 Therefore, x--1=x+1is a factor of both numerator and denominator

Therefore, the possible function is

fx=a(x-1)(x+1)(x-4)(x+1)

Now to find ause limx→-1⁡f(x)=2

⇒limx→-1⁡a(x-1)(x+1)(x-4)(x+1)=2

Simplify,

⇒limx→-1⁡a(x-1)(x-4)=2

Apply limit,

⇒a(-1-1)(-1-4)=2

Simplify,

⇒-2a-5=2

Solving for a

⇒a=5

Therefore, function will be fx=5(x-1)(x+1)(x-4)(x+1)

At x=0

f0=5(0-1)(0+1)(0-4)(0+1)

=5(-1)(1)(-4)(1)

Simplify,

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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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(a) Give examples of functions that a:e continuous on [ 1, 1]. (b) Give an example of a function that is not co...

Single Variable Calculus: Early Transcendentals

15. Trophy Masters had net sales for the year of $145,000. The beginning inventory at retail was $36,000. and t...

Contemporary Mathematics for Business & Consumers

True or False Label each of the following statements as either true or false. 2. Any two abelian groups of the ...

Elements Of Modern Algebra

Draw each of the following angles in standard position and then name the reference angle. 19510

Trigonometry (MindTap Course List)

Sometimes, Always, or Never: The antiderivative of an elementary function is elementary.

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

Think About It In Exercises 93-96, create a function whose graph has the given characteristics. (There is more ...

Calculus: Early Transcendental Functions (MindTap Course List)

True or False: If dz exists at (x, y), then z = f(x, y) is differentiable at (x, y).

Study Guide for Stewart's Multivariable Calculus, 8th

LIGHTNING DEATHS According to date obtained from the National Weather Service, 376 of the 439 people killed by ...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 1 to 6, state the hypothesis H and the conclusion C for each statement. Two angles are congruent i...

Elementary Geometry for College Students

Finding a Derivative In Exercises 29-40, Find the derivative of the algebraic function. f(x)=21xx3

Calculus

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

Calculus (MindTap Course List)

Describing a Region In Exercises 58, use polar coordinates to describe the region shown.

Multivariable Calculus

Explain how holding a participant variable such as gender constant prevents the variable from becoming a confou...

Research Methods for the Behavioral Sciences (MindTap Course List)

For the data in the previous exercise, subtract 10 from each sample observation. For the new set of values, cal...

Introduction To Statistics And Data Analysis

Morningstar tracks the performance of a large number of companies and publishes an evaluation of each. Along wi...

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

Express each percent as a decimal fraction or mixed decimal. 43. 238

Mathematics For Machine Technology

Practice Solve each logarithmic equation. 12log4x+5=logx

College Algebra (MindTap Course List)

A study reported in the Journal of Small Business Management concluded that self-employed individuals do not ex...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Identify the circumstances in which it is useful to write a research proposal before conducting the actual rese...

Research Methods for the Behavioral Sciences (MindTap Course List)

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