Question

Use Newton's method to approximate a root of the equation $e^{0.9x^2} = 6 - x$ as follows. Let $x_1 = 2$ be the initial approximation. The second approximation $x_2$ is and the third approximation $x_3$ is

          Use Newton's method to approximate a root of the equation $e^{0.9x^2} = 6 - x$ as follows.
Let $x_1 = 2$ be the initial approximation.
The second approximation $x_2$ is
and the third approximation $x_3$ is
        
Use Newton's method to approximate a root of the equation e^0.9x^2 = 6 - x as follows.
Let x1 = 2 be the initial approximation.
The second approximation x2 is
and the third approximation x3 is

Added by Adam B.

Close

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Let =2 be the initial approximation. The second approximation is and the third approximation is
Close icon
Play audio
Feedback
Powered by NumerAI
Ivan Kochetkov Kathleen Carty
Danielle Fairburn verified

Jason Horton and 85 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
2-134

2.

Jason H.

2-134

2.

Jason H.

use-newton-method-to-find-the-second-and-third-approximation-of-a-root-of-5-sinc-starting-with-1-1as-the-initial-approximation-the-second-approximation-is-t2-the-third-approximation-is-t3-18547

Use Newton's method to find the second and third approximation of a root of 5 sin(x) = x starting with x1 = 1 as the initial approximation. The second approximation is x2 = . The third approximation is x3 = .

Frank D.


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,875 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,187 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,614 solutions

*

Transcript

-
00:01 Alright, in your question, you're asked to use newton's method to approximate the root for the following function.
00:07 I have newton's method laid out there for you to see.
00:11 One of the things we're going to need is the derivative of our function.
00:15 So f prime of x is going to equal, you just multiply the 3 to the 2, 6x, and you drop the power by 1 plus 8.
00:25 And then the derivative of 2 is just a 0.
00:29 Okay, you're told to start with your first iteration, x sub 1, to be negative 1.
00:35 So if we're interested in x sub 2, which is n plus 1, we're going to take our x sub 1 value and subtract f of x sub 1 divided by f prime of x sub 1.
00:51 So x sub 2 is going to equal x sub 1, which is negative 1, minus f of negative 1, divided by f prime of negative 1.
01:06 Okay, so negative 1 minus f of negative 1, if i put a negative 1 into the f function, i end up with a negative 8 over f prime of negative 1 is a 14...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever