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

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Chapter 8.4, Problem 45E
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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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Finding an Equation of a Tangent Line In Exercises 43–50, find an equation of the tangent line to the graph of the function at the given point.

Function Point y = sin   8 x ( π ,   0 )

To determine

To calculate: The equation of the tangent line to the graph of the provided function y=sin8x at given point (π,0).

Explanation

Given Information:

The provided function is y=sin8x at given point (π,0).

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

General power rule of differentiation:

ddx[xn]=nxn−1

Write the equation of the tangent line at a given point (x1,y1).

y−y1=dydx(x1,y1)(x−x1)

Here, dydx(x1,y1) represents slope at point (x1,y1).

Calculation:

Consider the provided function:

y=sin8x

Differentiate the above function using Sine and general power rules of differentiation.

dydx=ddx[sin8x]=8cos8x

The derivative of function y=sin8x

dydx=8cos8x

Substitute, π for x in above derivative

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

Finding Vertical Asymptotes In Exercises 7378, find the vertical asymptotes (if any) of the graph of the functi...

Calculus (MindTap Course List)

Area In Exercises 61 and 62, use a line integral to find the area of the region R R: Region bounded by the grap...

Multivariable Calculus

If , then the vector field F is: linear conservative gradient tangent

Study Guide for Stewart's Multivariable Calculus, 8th

Sketching a Derivative In Exercises 43-48, sketch the graph of f Explain how you found your answer.

Calculus

A sample of size 100 is selected from a population with p = .40. a. What is the expected value of p? b. What is...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Will improving customer service result in higher stock prices for the companies providing the better service? W...

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

A workpiece or tool with a diameter of 0.750" turns at 350 revolutions per minute. Use C=3.1416DN12 or DN12 to ...

Mathematics For Machine Technology

Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry...

College Algebra (MindTap Course List)

What elements are required for a single-case research study to qualify as an experiment?

Research Methods for the Behavioral Sciences (MindTap Course List)

In addition to the key words, you should also be able to define each of the following terms: Ethics Nuremberg C...

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider the scatterplot of acrylamide concentration versus frying time from the previous exercise. a. Which ob...

Introduction To Statistics And Data Analysis

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