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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.4, Problem 23E
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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
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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

9-32 Find the limit or show that it does not exist.

lim x →   ∞ ( x 2 + a x − x 2 + b x )

To determine

To find:

limx⟶∞⁡(x2+ax-x2+bx)

Explanation

1) Concept:

To evaluate the limit at infinity of any rational function, first divide both the numerator and denominator by the highest power of x that occurs in the denominator.

2) Formula:

i) Quotient law:limx ⟶∞⁡p(x)q(x)= limx ⟶∞p(x)limx ⟶∞q(x)

ii) Sum law: limx → ∞⁡[px+qx]=limx → ∞⁡p(x)+limx → ∞⁡q(x)

iii) Difference law: limx → ∞⁡[px-qx]=limx → ∞⁡p(x)-limx → ∞⁡q(x)

iv) Constant law: limx → ∞⁡c =c

v) Constant multiple law: limx → ∞⁡c p(x)=climx → ∞⁡ p(x)

3) Given:

limx⟶∞⁡(x2+ax-x2+bx)

4) Calculation:

Multiply numerator and denominator by (x2+ax+x2+bx),

limx⟶∞⁡(x2+ax-x2+bx)=limx⟶∞x2+ax-x2+bxx2+ax+x2+bxx2+ax+x2+bx

=limx⟶∞x2+ax-x2-bxx2+ax+x2+bx

=limx⟶∞

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Frontier Homes, Inc., a builder of custom homes, owns 12612 acres of undeveloped land. If the property is divid...

Contemporary Mathematics for Business & Consumers

For Questions 1 through 8, fill in each blank with the appropriate word or number. Two angles are ________ if t...

Trigonometry (MindTap Course List)

In Exercises 1324, prove the statements concerning the relation on the set Z of all integers. If 0xy, then x2y...

Elements Of Modern Algebra

The area of the region bounded by , , and r = sec θ is:

Study Guide for Stewart's Multivariable Calculus, 8th

The appropriate option for the value of (123).

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

Evaluating a Function In Exercises 110, evaluate the function at the given value(s) of the independent variable...

Calculus: Early Transcendental Functions (MindTap Course List)

What type of quadrilateral ABCD is represented if its vertices are A0,0, Ba,0, Ca+b,c, and Db,c?_

Elementary Geometry for College Students

In Exercises 2730, fill in the missing entries by performing the indicated row operations to obtain the row-red...

Finite Mathematics for the Managerial, Life, and Social Sciences

Using a p -Series Ten terms are used to approximate a convergent p-series. Therefore, the remainder is a functi...

Calculus

EXPLORING CONCEPTS PlanesConsider a line and a point not on the line. How many planes contain the line and the ...

Multivariable Calculus

Using Lagrange Multipliers In Exercises 3-10, use Lagrange multipliers to find the indicated extrema, assuming ...

Calculus (MindTap Course List)

Tower of Hanoi A well-known problem in mathematics is The Tower of Hanoi, first attributed to Edouard Lucas in ...

College Algebra (MindTap Course List)

If a hurricane was headed your way, would you evacuate The headline of a press release issued January 21 2009 b...

Introduction To Statistics And Data Analysis

Annual retail store revenue for Apple from 2007 to 2014 are shown below (source: ifoapple.com). Year Period Ret...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Multiply: 12.3457.86 .

Mathematics For Machine Technology

In a manufacturing process the assembly line speed (feet per minute) was thought to affect the number of defect...

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

Identify the appropriate hypothesis test for each of the following research situations. a. A researcher conduct...

Research Methods for the Behavioral Sciences (MindTap Course List)

What elements are required for a single-case research study to qualify as an experiment?

Research Methods for the Behavioral Sciences (MindTap Course List)

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