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Math
CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.R, Problem 23E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1CC
Problem 2CC
Problem 3CC
Problem 4CC
Problem 5CC
Problem 6CC
Problem 7CC
Problem 8CC
Problem 9CC
Problem 10CC
Problem 11CC
Problem 1TFQ
Problem 2TFQ
Problem 3TFQ
Problem 4TFQ
Problem 5TFQ
Problem 6TFQ
Problem 7TFQ
Problem 8TFQ
Problem 9TFQ
Problem 10TFQ
Problem 11TFQ
Problem 12TFQ
Problem 13TFQ
Problem 14TFQ
Problem 15TFQ
Problem 16TFQ
Problem 17TFQ
Problem 18TFQ
Problem 19TFQ
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
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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
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Problem 68E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

17-28 Use the guidelines of Section 3.5 to sketch the curve.

y = ( x − 1 ) 3 x 2

To determine

To sketch:

The graph of the function y=x-13x2

Explanation

1) Concept:

 i) A domain is the set of x values that satisfy the function.

ii) To find x-intercept, put y=0, and to find y-intercept, put x=0 in the given function.

iii) Symmetry: To find symmetry, replace x by –x and check the behaviour of function. Thus, if f-x=fx, then it is an even function, so it has y-axis symmetry. If f-x=-fx, then it is an odd function, so it has x-axis symmetry. And if f-x≠-fx≠fx, then it has no symmetry.

iv) An asymptote is a tangent at infinity. To find horizontal, vertical, and slant asymptote, follow the rules.

v) A function is increasing if f'x>0  and decreasing if f'x<0 in that particular interval.

vi) The number f(c) is a local maximum value of f  if fc≥f(x) when x is near c and is a local minimum value of f if fc≤ f(x) when x is near c.

vii) If f''x>0, the function is concave up and if f''x<0, the function is concave down in that particular interval. And if f''x=0, give the values of inflection points

2) Given:

The function y=x-13x2

3) Calculation:

The given function is y=x-13x2

A) Domain

The domain is a set of all values of x except when the denominator is zero.

Here x2=0  becomes x=0

Therefore, the domain of the function is (-∞, 0)∪(0, ∞)

B) Intercepts

For y– intercept, plug x=0  in the given function and solve it

As the function is not defined for x=0, it has no y-intercept.

Now for x-intercept set y = 0 then equation becomes

x-13x2=0

x-13 =0 

x=1

  Therefore, x-intercept is x=1

C) Symmetry

For symmetry replace x by (-x)

f(-x)=-x-13(-x)2

Since, f-x≠-fxand fx≠f(-x)

That means there is no symmetry

Therefore f is neither an even nor an odd function

D) Asymptote

limx→±∞ ⁡x-13<

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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
Sect-3.1 P-11ESect-3.1 P-12ESect-3.1 P-13ESect-3.1 P-14ESect-3.1 P-15ESect-3.1 P-16ESect-3.1 P-17ESect-3.1 P-18ESect-3.1 P-19ESect-3.1 P-20ESect-3.1 P-21ESect-3.1 P-22ESect-3.1 P-23ESect-3.1 P-24ESect-3.1 P-25ESect-3.1 P-26ESect-3.1 P-27ESect-3.1 P-28ESect-3.1 P-29ESect-3.1 P-30ESect-3.1 P-31ESect-3.1 P-32ESect-3.1 P-33ESect-3.1 P-34ESect-3.1 P-35ESect-3.1 P-36ESect-3.1 P-37ESect-3.1 P-38ESect-3.1 P-39ESect-3.1 P-40ESect-3.1 P-41ESect-3.1 P-42ESect-3.1 P-43ESect-3.1 P-44ESect-3.1 P-45ESect-3.1 P-46ESect-3.1 P-47ESect-3.1 P-48ESect-3.1 P-49ESect-3.1 P-50ESect-3.1 P-51ESect-3.1 P-52ESect-3.1 P-53ESect-3.1 P-54ESect-3.1 P-55ESect-3.1 P-56ESect-3.1 P-57ESect-3.1 P-58ESect-3.1 P-59ESect-3.1 P-60ESect-3.1 P-61ESect-3.1 P-62ESect-3.1 P-63ESect-3.1 P-64ESect-3.1 P-65ESect-3.1 P-66ESect-3.1 P-67ESect-3.1 P-68ESect-3.1 P-69ESect-3.1 P-70ESect-3.1 P-71ESect-3.1 P-72ESect-3.2 P-1ESect-3.2 P-2ESect-3.2 P-3ESect-3.2 P-4ESect-3.2 P-5ESect-3.2 P-6ESect-3.2 P-7ESect-3.2 P-8ESect-3.2 P-9ESect-3.2 P-10ESect-3.2 P-11ESect-3.2 P-12ESect-3.2 P-13ESect-3.2 P-14ESect-3.2 P-15ESect-3.2 P-16ESect-3.2 P-17ESect-3.2 P-18ESect-3.2 P-19ESect-3.2 P-20ESect-3.2 P-21ESect-3.2 P-22ESect-3.2 P-23ESect-3.2 P-24ESect-3.2 P-25ESect-3.2 P-26ESect-3.2 P-27ESect-3.2 P-28ESect-3.2 P-29ESect-3.2 P-30ESect-3.2 P-31ESect-3.2 P-32ESect-3.2 P-33ESect-3.2 P-34ESect-3.2 P-35ESect-3.2 P-36ESect-3.3 P-1ESect-3.3 P-2ESect-3.3 P-3ESect-3.3 P-4ESect-3.3 P-5ESect-3.3 P-6ESect-3.3 P-7ESect-3.3 P-8ESect-3.3 P-9ESect-3.3 P-10ESect-3.3 P-11ESect-3.3 P-12ESect-3.3 P-13ESect-3.3 P-14ESect-3.3 P-15ESect-3.3 P-16ESect-3.3 P-17ESect-3.3 P-18ESect-3.3 P-19ESect-3.3 P-20ESect-3.3 P-21ESect-3.3 P-22ESect-3.3 P-23ESect-3.3 P-24ESect-3.3 P-25ESect-3.3 P-26ESect-3.3 P-27ESect-3.3 P-28ESect-3.3 P-29ESect-3.3 P-30ESect-3.3 P-31ESect-3.3 P-32ESect-3.3 P-33ESect-3.3 P-34ESect-3.3 P-35ESect-3.3 P-36ESect-3.3 P-37ESect-3.3 P-38ESect-3.3 P-39ESect-3.3 P-40ESect-3.3 P-41ESect-3.3 P-42ESect-3.3 P-43ESect-3.3 P-44ESect-3.3 P-45ESect-3.3 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Probability and Statistics for Engineering and the Sciences

Statistical Literacy For a binomial experiment, how many outcomes are possible for each trial? What are the pos...

Understanding Basic Statistics

Convert the expressions in Exercises 31-36 to positive exponent form. 3x4

Finite Mathematics

Concept Quiz 2.1 For Problems 1-10, answer true or false. Equivalent equations have the same solution set.

Intermediate Algebra

Student Demographics A college finds that 841 of its students are receiving financial aid, 525 students are bus...

Mathematical Excursions (MindTap Course List)

Fill in each blank: 3qt=pt

Elementary Technical Mathematics

A lawn roller in the shape of a right circular cylinder has a radius of length 18 in. and a length height of 4 ...

Elementary Geometry For College Students, 7e

CHECKPOINT 1. Suppose that $500 is deposited at the end of every quarter for 6 years in an account that pays 8%...

Mathematical Applications for the Management, Life, and Social Sciences

Find f. f(t) = t + 1/t3, t 0, f(1) = 6

Single Variable Calculus: Early Transcendentals

Finding Extrema on a Closed Interval In Exercises 23-40, find the absolute extrema of the function on the close...

Calculus of a Single Variable

Show that each pair of sectors is perpendicular. 2i+j and i2j

Trigonometry (MindTap Course List)

Perform the indicated operation for the following. $78.14-$9.52

Contemporary Mathematics for Business & Consumers

In Exercises 13 and 14, part of the multiplication table for the group G={ a,b,c,d } is given. In each case, co...

Elements Of Modern Algebra

Find for y defined implicity by .

Study Guide for Stewart's Multivariable Calculus, 8th

Verifying Divergence In Exercises 11-18, verify that the infinite series diverges. n=04(1.05)n

Calculus: Early Transcendental Functions (MindTap Course List)

The third partial sum of is:

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

Find the distance between each pair of points: a 0,-3 and 4, 0 c 3, 2 and 5,-2 b -2, 5 and 4,-3 d a,0 and 0,b

Elementary Geometry for College Students

THE SOCIAL LADDER The following table summarizes the results of a poll conducted with 1154 adults. Annual House...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding a Limit In Exercises 5-22, find the limit. limx55x+3

Calculus

True or False? In Exercises 91-96, determine whether the statement is true or false. If it is false, explain wh...

Calculus (MindTap Course List)

Using Different Methods In Exercises 19-22, find w/ s and w/ t (a) by using the appropriate Chain Rule and ...

Multivariable Calculus

Express these ratios in lowest fractional form. 6. 45in.:27in.

Mathematics For Machine Technology

Corporate triple-A bond interest rates for 12 consecutive months follow. 9.59.39.49.69.89.79.810.59.99.79.69.6 ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Slopes R Us needs to borrow 120,000 to increase its inventory of ski equipment for the upcoming season. The own...

Mathematics: A Practical Odyssey

An accounting firm works for a number of clients in the banking, insurance, and brokerage industries: N1 = 50 b...

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

The data on the next page on pre- and postoperative lung capacities for 22 patients who underwent surgery as tr...

Introduction To Statistics And Data Analysis

A researcher finds that college students are more anxious near final exams in December than at the beginning of...

Research Methods for the Behavioral Sciences (MindTap Course List)

Find all rational zeros of each polynomial function. P(x)=36x4x2+2x1

College Algebra (MindTap Course List)

Identify the characteristics that differentiate different sets of data and identify the hypothesis test(s) appr...

Research Methods for the Behavioral Sciences (MindTap Course List)

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