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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8.3, Problem 57E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Evaluating a Trigonometric Limit In Exercises 53–62, complete the table to estimate lim x → 0 f ( x ) . Use a graphing utility (set in radian mode) to graph the function and confirm your result. See Example 4.

x -0.1 -0.01 -0.001 0.001 0.01 0.1
f(x)

f ( x ) = 3 ( 1 − cos   x ) x

To determine

To calculate: The estimated value of limx→0f(x) for the function f(x)=3(1−cosx)x by completing the following table:

x−0.1−0.01−0.0010.0010.010.1f(x)

Also confirm the result by use of graphical utility.

Explanation

Given Information:

The trigonometric function is, f(x)=3(1−cosx)x.

Formula used:

Limit of a function exit at a point if the left-hand limit, right hand limit and the function itself has approximately same value.

Calculation:

To estimate the value of limx→0f(x), substitute the different values of x from the given table in the function f(x)=3(1−cosx)x to get the complete table:

x−0.1−0.01−0.0010.0010.010.1f(x)−0.1499−0.0150−0.00150.00150.01500.1499

Now, Calculate the value of limx→0f(x):

From the table, it can be clearly seen that the value of limx→03(1−cosx)x=0.

Therefore, the value of limx→03(1−cosx)x=0

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
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Perform the indicated operations: 65+42

Elementary Technical Mathematics

Finding Points of Intersection In Exercises 27-34, find the points of intersection of the graphs of the equatio...

Calculus: Early Transcendental Functions (MindTap Course List)

Matching In Exercises 5-8, match the Taylor polynomial approximation of the function f(x)=ex2/2 with its graph....

Calculus of a Single Variable

DRUG DOSAGES FOR CHILDREN A method sometime used by pediatricians to calculate the dosage of medicine for child...

Finite Mathematics for the Managerial, Life, and Social Sciences

Does a isosceles trapezoid have a an incenter?.b a circumcenter?

Elementary Geometry for College Students

Let f(x)={2x2forx13forx1. Which limit does not exist? a) limx3f(x) b) limx1+f(x) c) limx1f(x) d) limx1f(x)

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Multivariable Calculus

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Calculus (MindTap Course List)

True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

Finding the Center of Mass Find the center of mass of the lamina in Exercise 31 when the circular portion of th...

Calculus

A process that is in control has a mean of = 12.5 and a standard deviation of = .8. a. Construct the x contro...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Refer to the Costello Music Company problem in exercise 49. a. Using time series decomposition, compute the sea...

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

Describe the major elements of the APA ethical guidelines for nonhuman subjects in research.

Research Methods for the Behavioral Sciences (MindTap Course List)

The article Effects of Age on the Variability and Stability of Gait: A Cross-Sectional Treadmill Study in Healt...

Introduction To Statistics And Data Analysis

For each exercise, functions of two angles are given. Which of the functions of the two angles is greater? Do n...

Mathematics For Machine Technology

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)

Practice Determine whether each function is one-to-one. fx=12x

College Algebra (MindTap Course List)

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