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

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Chapter 8.3, Problem 56E
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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 ) = 1 − cos   2 x x

To determine

To calculate: The estimated value of limx→0f(x) for the function f(x)=1−cos2xx 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)=1−cos2xx.

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)=1−cos2xx to get the complete table:

x−0.1−0.01−0.0010.0010.010.1f(x)−0.1993−0.0200−0.0020.0020.02000.1993

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

From the table, it can be clearly seen that the value of limx→01−cos2xx=0.

Therefore, the value of limx→01−cos2xx=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
Sect-8.1 P-7SWUSect-8.1 P-8SWUSect-8.1 P-9SWUSect-8.1 P-10SWUSect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10ESect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.1 P-57ESect-8.1 P-58ESect-8.2 P-1CPSect-8.2 P-2CPSect-8.2 P-3CPSect-8.2 P-4CPSect-8.2 P-5CPSect-8.2 P-6CPSect-8.2 P-7CPSect-8.2 P-1SWUSect-8.2 P-2SWUSect-8.2 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TABLE 21-1 Magnum Enterprises Six-Month Sales Report Magnum Enterprise Six-Month Sale Report January February...

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The general solution to y″ − 6y′ + 8y = 0 is: y = ex(c1 cos 4x + c2 sin 4x) y = e4x(c1 cos x + c2 sin x) y = c1...

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True or False: converges absolutely.

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Explain the advantages and disadvantages of a stratified random sample compared with a proportionate stratified...

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Although studies continue to show smoking leads to significant health problems, 20% ofadults in the United Stat...

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Factor each expression completely, if possible. 6x2+7x24

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Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 16 11 17 14 a. Construct a time series pl...

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