1 / 8

4.5: Linear Approximations, Differentials and Newton’s Method

4.5: Linear Approximations, Differentials and Newton’s Method. Greg Kelly, Hanford High School, Richland, Washington. We call the equation of the tangent the linearization of the function.

ula
Download Presentation

4.5: Linear Approximations, Differentials and Newton’s Method

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4.5: Linear Approximations, Differentials and Newton’s Method Greg Kelly, Hanford High School, Richland, Washington

  2. We call the equation of the tangent the linearization of the function. For any function f (x), the tangent is a close approximation of the function for some small distance from the tangent point.

  3. is the standard linear approximation of f at a. Start with the point/slope equation: linearization of f at a The linearization is the equation of the tangent line, and you can use the old formulas if you like.

  4. Differentials: When we first started to talk about derivatives, we said that becomes when the change in x and change in y become very small. dy can be considered a very small change in y. dx can be considered a very small change in x.

  5. Let be a differentiable function. The differential is an independent variable. The differential is:

  6. Example: Consider a circle of radius 10. If the radius increases by 0.1, approximately how much will the area change? very small change in r very small change in A (approximate change in area)

  7. (approximate change in area) Compare to actual change: New area: Old area:

More Related