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Problem

Use Newton's method to find the coordinates, corr…

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Problem 38 Hard Difficulty

Of the infinitely many lines that are tangent to the curve $ y = -\sin x $ and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.


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Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Related Topics

Derivatives

Differentiation

Volume

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04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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06:14

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Watch More Solved Questions in Chapter 4

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42

Video Transcript

questions. They're here. We are looking at that with X equal sign of vets therefore f frying equal. Negative, right is negative. Sign this equals negative co sign. No, thanks. What I wanted at the giving us crying of a what? He will Negative co sign. Hey, well, so far Slope are smooth, of course is by two minus by one over X two minus x one. So I would have a sign of a negative sign of a minus zero. Looking yours over a minus zero, which is negative. Sign of egg over a. And if I want a lying tangent two at a I'm gonna set this flow. Negative sign of a over a equal to my derivative. So I have negative co sign of a equals negative sign of a over a And then I'm gonna solve for a So I get a equals a holes sign over co sign, and that's actually get a positive sign. Overcoat size. A sign of a over co sign of a which, of course, is Qianjin of a Yeah, okay. And now we're used a Newton's nothing so g of X is gonna equal 10 of X. That's an X with eggs minus X. And then when I take the derivative of that I seek, it's where X minus one. So now I'm going to put into my graphing calculator this into by one and this into y two. And then I put Oh, and it's one ex my news g mine g over Prime, Which in my calculator waas Um why one over Why, too? So in why three I put X minus. Why one divide by y two. And then I got, uh, except one. He started with 4.5 from the grass. Thanks to you, I got four point or nine 36 14 That's a three like that. Or pointy or nine. 3410 four for we for nine, 34 03 And then you answer the question. I did f prime of four point or nine three or zero. And that gave me 0.217 23 Water

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Related Topics

Derivatives

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Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

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Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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