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

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Chapter 8.4, Problem 41E
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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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Slope of a Tangent Line In Exercises 41 and 42, find the slope of the tangent line to the given sine function at the origin. What can you conclude about the slope of the sine function sin ax at the origin?

(a)  y = sin x                   (b)  y = sin 2 x

Chapter 8.4, Problem 41E, Slope of a Tangent Line In Exercises 41 and 42, find the slope of the tangent line to the given sine

(a)

To determine

To calculate: The slope of the tangent line to the graph of the provided sine function y=sinx at the origin and provided its graph, which is shown below as:

Calculus: An Applied Approach (MindTap Course List), Chapter 8.4, Problem 41E , additional homework tip 1

Explanation

Given Information:

The provided function is y=sinx and its graph is shown below as:

Formula used:

Sine differentiation rule:

ddx[sinu]=cosududx

General power rule of differentiation:

ddx[xn]=nxn−1

Calculation:

Consider the provided function:

y=sinx

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

(b)

To determine

To calculate: The slope of the tangent line to the graph of the provided sine function y=sin2x at the origin and provided its graph, which is shown below as:

Calculus: An Applied Approach (MindTap Course List), Chapter 8.4, Problem 41E , additional homework tip 2

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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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Graphing a Plane Curve In Exercises 5966, use a graphing utility to graph the curve represented by the parametr...

Calculus (MindTap Course List)

Area and Perimeter A semicircle is on top of a rectangle (see figure). When the area is fixed and the perimeter...

Calculus

True or False: converges.

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

A critical point of f(x, y) = 60 − 6x + x2 + 8y − y2 is: (3, 4) (23, 24) (−3, 4) (3, −4)

Study Guide for Stewart's Multivariable Calculus, 8th

PBS News Hour reported that 39.4% of Americans between the ages of 25 and 64 haveat least a two-year college de...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In Exercises 63-66, match each variation equation on the left with a variation sentence on the right./i M=knp4 ...

College Algebra (MindTap Course List)

Suppose that you will take a multiple-choice exam consisting of 100 questions with five possible responses to e...

Introduction To Statistics And Data Analysis

Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empir...

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

Define a construct and explain the role that constructs play in theories.

Research Methods for the Behavioral Sciences (MindTap Course List)

Substitute the given numbers for letters in the following expressions and solve. 5e3+(efd)(d)3;d=10.55,e=8.26,f...

Mathematics For Machine Technology

Explain how researchers identify a “significant” difference between two phases in a single-case study.

Research Methods for the Behavioral Sciences (MindTap Course List)

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