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

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Chapter 8.3, Problem 58E
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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 ) = 2 sin ( x / 4 ) x

To determine

To calculate: The estimated value of limx→0f(x) for the function f(x)=2sin(x4)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)=2sin(x4)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)=2sin(x4)x to get the complete table:

x−0.1−0.01−0.0010.0010.010.1f(x)0.49990.50000.50.50.50000.4999

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

From the table, it can be clearly seen that the value of limx→02sin(x4)x=12.

Therefore, the value of limx→02sin(x4)x=12

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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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Elementary Geometry For College Students, 7e

Finding the Equation of a Sphere In Exercises 3740, find the standard equation of the sphere. Center: (0, 2, 5)...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding Points of Inflection In Exercises 17-32, find the points of inflection and discuss the concavity of the...

Calculus of a Single Variable

In Exercises 9-12, refer to the following matrices, and perform the indicated operations. Round your answers to...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 3 to 8, use the drawing provided. Given: Obtuse ABC Construct: The perpendicular bisector of AC-

Elementary Geometry for College Students

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