1 / 7

4.8 - Differentials

4.8 - Differentials. Linear (or Tangent Line) Approximations. For values close to a , . Linear Approximation – Examples. Determine the linearization (another name for linear approximation) of f ( x ) = ln x at a = 1. Find the linear approximation of the function .

chesmu
Télécharger la présentation

4.8 - Differentials

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. 4.8 - Differentials

  2. Linear (or Tangent Line) Approximations For values close to a,

  3. Linear Approximation – Examples Determine the linearization (another name for linear approximation) of f (x) = ln x at a = 1. Find the linear approximation of the function And use it to approximate the numbers and

  4. Differentials Up to now, we’ve thought of dy/dx as notation for a derivative. We can think of dx and dy as separate quantities called differentials.

  5. Differentials We can now think of dy/ dx as a ratio of two quantities (the differential of y and the differential of x). So for a given change in x (dx) we can calculate a change in y (dy).

  6. Differentials – Example 1 Find the differential dy and evaluate dy for the given values of x and dx.

  7. Differentials – Example 2 You may have used this concept when calculating errors in measurements or calculations. The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (b) What is the relative errors (dA / A)

More Related