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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.4, Problem 25E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

lim x → 0 1 + 2 x − 1 − 4 x x

To determine

To evaluate: The value of   limx→01+2x−1−4xx .

Explanation

Obtain the value of the function as x approaches 0 .

As x approaches 0 , the numerator is,

1+2x−1−4x=1+2⋅(0)−1−4⋅(0)=1+0−1−0=1−1=0

As x approaches 0 , the denominator x is also 0 .

Thus, limx→01+2x−1−4xx=00 is in an indeterminate form.

Therefore, apply L’Hospital’s Rule and obtain the limit as shown below

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Chapter 4.4,
Problem 24E
Chapter 4.4,
Problem 26E
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Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an bn for all n, ...

Single Variable Calculus: Early Transcendentals

Winding a Chain In Exercises 29-32, consider a 20-foot chain that weighs 3 pounds per foot hanging from a winch...

Calculus of a Single Variable

Identifying and Sketching a Conic In Exercises 113-118, find the eccentricity and the distance from the pole to...

Calculus: Early Transcendental Functions (MindTap Course List)

The accompanying tree diagram represents an experiment consisting of two trials.Use the diagram to find: a. P(A...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercise 5 to 9, use a compass and a straightedge to complete the constructions. Given: AB Construct: The pe...

Elementary Geometry for College Students

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

Calculus

True or False: If converges absolutely, then it converges conditionally.

Study Guide for Stewart's Multivariable Calculus, 8th

A number c that satisfies the Mean Value Theorem for f(x) = x3 on [1, 4] is: a) 7 b) 12 c) 63 d) 63

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

Finding Volume Using a Change of Variables In Exercises 23-30, use a change of variables to find the volume of ...

Multivariable Calculus

Find f(1) and f(2). f(x)=xx1

College Algebra (MindTap Course List)

Express the following degrees and minutes as decimal degrees. Round the answer to 2 decimal places. 610'

Mathematics For Machine Technology

The cost of consumer purchases such as single-family housing, gasoline, Internet services, tax preparation, and...

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

Write a research report using APA style.

Research Methods for the Behavioral Sciences (MindTap Course List)

Make a list of five ideas for a general research topic that interests you. For each, identify the source of the...

Research Methods for the Behavioral Sciences (MindTap Course List)

The article Predicting Marathon Time from Anaerobic Threshold Measurements (The Physician and Sports Medicine [...

Introduction To Statistics And Data Analysis

Consider the following hypothesis test. H0:12=22Ha:1222 a. What is your conclusion if n1 = 21, s12=8.2, n2 = 26...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Building Design The cross section of a precast concrete beam for a building is bounded by the graphs of the equ...

Calculus (MindTap Course List)

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