1 / 5

Differentials Continued

Differentials Continued. Comparing dy and  y  y is the actual change in y from one point to another on a function (y 2 – y 1 ) d y is the corresponding change in y on the tangent line dy = f’(x) dx d y is often used to approximate  y. Given points P and Q on function f.

fruma
Download Presentation

Differentials Continued

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. Differentials Continued Comparing dyand y • y is the actual change in y from one point to another on a function (y2 – y1) • dy is the corresponding change in y on the tangent line dy = f’(x)dx • dy is often used to approximate y

  2. Given points P and Q on function f. The slope between P and Q is y / x The slope of the tangent line at P is dy/dx Notice: dx = xand dy ≈ y Q P

  3. Example 1 Find both y and dy and compare. y = 1 – 2x2at x = 1 when x= dx = -.1 Solution: y = f(x + x) – f(x) = f(.9) – f(1) = -.62 – (-1) = .38 dy = f’(x)dx = (-4)(-.1) = .4 ** Note that y ≈ dy

  4. Example 2 The radius of a ball bearing is measured to be .7 inches. If the measurement is correct to within .01 inch, estimate the propagated error in the volume V of the ball bearing. ** Propagated error means the resulting change, or error, in measurement

  5. Example 2 Continued To decide whether the propagated error is small or large, it is best looked at relative to the measurement being calculated. • Find the relative error in volume of the ball bearing. ** Relative error is dy/y, or in this case dV/V • Find the percent error,(dV/V)*100.

More Related