Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Follow the instructions for Exercise 1(a) but use $ x_1 = 1 $ as the starting approximation for finding the root $ r $.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Yuki Hotta

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

00:20

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Derivatives

Differentiation

Volume

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:35

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.

06:14

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.

0:00

Follow the instructions fo…

01:14

00:59

Jollow the instructions fo…

01:15

02:05

Find linear approximation …

02:07

For the following exercise…

03:23

Use the linear approximati…

02:13

Use Newton's method w…

09:40

03:49

All right, let's go ahead and solve this problem. So Newton's method to approximate a route. So basically what the Newton methods do is this you're randomly first pick a point. For example, if I pick a point right here, the Y value is going to be located right there. Now, what I do is I draw a tangent line at that point and that is going to be my guest off the roof. Let's call it our one. Okay. Now, if that doesn't seem like it actually is the route I can actually continue now, what do I do? I actually plug in that point again. And now I get this height. Let's draw the tangent line going to look something like this. So here I can call it, are to. So as you can see, the second guess seems like it's going to be a better approximation to the actual word. Right now, this method seems like it worked really well for my choice of Let's call it are not, for example, I could have also done something like this. Now, this is a little bit artificial, but if I chose a point to be a root right here. Can you see that? This is the horizontal line right there. If I happen to choose a point where the tangent at the slope is going to be completely horizon tal, I will actually never reach a route anymore. So I won't be able to approximate anything. So that's one of the things about the Newton's method. If you don't get a good guess in the very first try, um, you might not actually get a really good estimation. However, I'm just going to still use this process in order to get to the solution or trying to answer the question that the book gives us. Okay, Now they are telling you what if my initial guess is one I'm going to call that X Not if X not is equal to one. I will start at this height Tangent line here. Looks like it's going to be something like this. So my guess is going to be when you actually draw that a little bit straight. It like this. Uh, There you go. That's a little better. Ah, still not the best drawing. But I can guess that the next point is going to be some around here that's avoiding the horizontal tangent, so it'll be pretty good. As you can see, it is going to be 123 maybe 3.2 or so. So that could be my first guess. And of course, my drawing is not really the most perfect. And there's no precise answer to this particular question because it's not like we're doing an analytical, um, calculation. So it's just all an estimate. Okay, so X one could be 3.2 Now. If I draw a tangent line from here, I can see that this is going to be my next guests x two. It's going to look like it's going to be about 1.8 or so if I want X three. Now I use this point. This one looks like it's gonna be a very good guess. So somewhere around there, maybe 2.4 or so let's call that X three. And when you plug in that value, you will see that the why is going to be very close to zero so you can decide to stop right there, or you can keep on moving and trying to find the next tangent line. So long story short. What you do is plug in the initial guests into the Y value, find the tangent line, and this point is going to be your guests for the for the route. And if you're not satisfied with that, you just continue on with the process. Okay, and that's the Newton's method.

View More Answers From This Book

Find Another Textbook

01:37

For three consecutive years the tuition of an university increased …

02:19

trillions of cubic gas production; points) The following table gives the ann…

01:18

Consider the function f (x) = 2 COSE) + 2) Determine its ampl…

03:05

Write an equation for Iina in point-slope form and slope-intercept …

03:30

Find all zeros of the polynomial: (Enter your answers as comma sepa…

03:46

Find the exact value of coscos 2cos 45" csc 46"csc 89<…

02:15

Each month, Victorias internet plan costs 50 dollars for the first 35 gigaby…

04:42

point) manufacturer ol downhill and cross-country skis reports- that manulac…

01:43

point) point P is often identified in mathematics using the notation P(x, Y)…

01:27

Consider the angle shown below with an initial ray pointing in the …