ap calculus bc 4 5 linearization and newton s method 2 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
AP Calculus BC – 4.5: Linearization and Newton’s Method - 2 PowerPoint Presentation
Download Presentation
AP Calculus BC – 4.5: Linearization and Newton’s Method - 2

Loading in 2 Seconds...

play fullscreen
1 / 7

AP Calculus BC – 4.5: Linearization and Newton’s Method - 2 - PowerPoint PPT Presentation


  • 195 Views
  • Uploaded on

AP Calculus BC – 4.5: Linearization and Newton’s Method - 2. Goals : Find linearizations and use Newton’s method to approximate the zeros of a function. Estimate the change in a function using differentials. Linearization: As long as it’s close, it’s close.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'AP Calculus BC – 4.5: Linearization and Newton’s Method - 2' - oleg-beck


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
ap calculus bc 4 5 linearization and newton s method 2

AP Calculus BC – 4.5: Linearization and Newton’s Method - 2

Goals: Find linearizations and use Newton’s method to approximate the zeros of a function.

Estimate the change in a function using differentials.

linearization as long as it s close it s close
Linearization: As long as it’s close, it’s close.

If f is differentiable at x = a, then the approximating function

is the linearization of f at a. The approximation f(x)≈ L(x) is the standard linear approximation of f at a. The point x = a is the center of the approximation.

newton s method newton raphson method
Newton’s Method (Newton-Raphson Method):

Newton’s Method is a numerical technique for approximating a zero of a function with zeros of its linearizations.

Procedure: 1.Guess a first approximation to a solution of the equation f(X) = 0. A graph of y = f(X) may help.

2. Iterate. Use the first approximation to get a second, and so on, using:

differentials
Differentials:

Differentials: Let y = f(x) be a differentiable function. The differential dx is an independent variable. The differential dy is dy = f’(x) dx.

Differential Estimate of Change: Let f(x) be differentiable at x = a. The approximate change in the value of f when x changes from a to a + dx is df = f’(a)dx.

absolute relative and percentage change
Absolute, Relative, and Percentage Change:

As we move from a to a nearby point a+dx:

True Estimated

Absolute Change

Relative Change

Percentage Change

assignments and notes
Assignments and Notes:
  • HW 4.5A: #3, 5-9, 11, 14, 15, 18.
  • HW 4.5B: #19, 22, 25, 27, 30, 33, 36, 39, 44, 50, 51. Look at #52.
  • Test next Thursday.