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CalculusCalculus10th Edition

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Chapter 10, Problem 52RE
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Horizontal and Vertical Tangency In Exercises 49-52, find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.

x = 2 − 2 cos θ ,   y = 2 sin 2 θ

To determine

To calculate: All points of horizontal and vertical tangency of the curve of x=2−2cosθ, y=2sin2θ and confirm your results using a graphing utility.

Explanation

Given:

The curve is x=2−2cosθ, y=2sin2θ.

Calculation:

Consider the given polar equation:

x=2−2cosθy=2sin2θ

Now, differentiating x and y with respect to θ.

Then,

dxdθ=ddθ(2−2cosθ)=ddθ(2)−ddθ(2cosθ)=2sinθ

And

dydθ=ddθ(2sinθ)=2ddθ(sinθ)=2cosθ

When dxdθ=0

2sinθ=0

That is,

sinθ=0

If sin(a)=b, then a=sin−1(b).

Therefore,

θ=sin−1(0)=0,π

When θ=0

x=2−2cos(0)=2−2(1)=0

When θ=π

x=2−2cos(π)=2−2(−1)=4

Thus, the vertical tangents are at (0,0), (4,0)

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A set of scores ranges from a high of X = 96 to a low of X = 27. If these scores are placed in a grouped freque...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 9 to 28, use the drawings as needed to answer the following questions. Suppose that planes M and N...

Elementary Geometry For College Students, 7e

To be accepted into an honor society, a student must have a grade-point average GPA in the top 10 of the school...

Essentials Of Statistics

1. Which of the following binomial probability distributions can be approximated accurately with a normal distr...

Mathematical Applications for the Management, Life, and Social Sciences

Critical Region Method: Student's t Solve Problem 9 using the critical region method of testing. Compare your c...

Understanding Basic Statistics

The membership graphs in the following figure provide definitions of (he fuzzy sets COLD and WARM. The point (3...

Mathematical Excursions (MindTap Course List)

Finding a Derivative In Exercises 5378, find the derivative of the function. h(x)=xsinx

Calculus: Early Transcendental Functions (MindTap Course List)

A regular tetrahedron is a regular triangular pyramid in which all faces lateral faces and base are congruent. ...

Elementary Geometry for College Students

IMPACT OF GAS PRICES ON CONSUMERS In a survey of 1012 adults aged 18 years and older conducted by Social Scienc...

Finite Mathematics for the Managerial, Life, and Social Sciences

Matching In Exercises 3-8, match the vector-valued function with its graph. [The graphs are labelled (a), (b), ...

Calculus (MindTap Course List)

Finding a Limit In Exercises 25-36, find the limit (if it exists). If the limit does not exist, explain why. li...

Multivariable Calculus

True or False: y = xex is a solution to y=y+yx.

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

The force needed for a 10-kg object to attain velocity 6t3i + 10tj is:

Study Guide for Stewart's Multivariable Calculus, 8th

Let P(x)=4x4+2x33x22. Find the remainder when P(x) is divided by each binomial. x+2

College Algebra (MindTap Course List)

Describe the advantages of a two-group design compared to an experiment with more than two groups.

Research Methods for the Behavioral Sciences (MindTap Course List)

The filling variance for boxes of cereal is designed to be .02 or less. A sample of 41 boxes of cereal shows a ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Consider the water temperature situation described in the previous exercise. a. For the hypotheses and test pro...

Introduction To Statistics And Data Analysis

Briefly explain what is meant when a researcher reports a significant mean difference between two treatment con...

Research Methods for the Behavioral Sciences (MindTap Course List)

Write 0.275 as a common fraction.

Mathematics For Machine Technology

The median annual income for families living in the United States is 56,200. Annual incomes in thousands of dol...

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

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