petra
Uploaded by
5 SLIDES
160 VUES
50LIKES

Calculating Rate of Change of Area in a Growing Circle

DESCRIPTION

Introducing a third variable, time, in determining the rate of change of the area of a circle as both the area and radius evolve over time. Utilizing implicit differentiation, find the derivative of the area with respect to time considering the changing radius.

1 / 5

Télécharger la présentation

Calculating Rate of Change of Area in a Growing Circle

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. Let’s introduce a “third” variable, time, t The Area of a circle is given by the formula The parameters are A and r

  2. Drop a pebble into a pond Both the Area and radius grow with respect to time

  3. Find the rate of change of the Area with respect to time That is, find:

  4. Notice, the variables do not agree This will be “implicit differentiation” with respect to t. When taking the derivative of A and r we will need to multiply by dA/dt and dr/dt respectively

  5. To find the rate of change of the area with respect to time, we need to know 2 things the radius, r, and its rate of change, dr/dt. This becomes a “related rate” problem in the next section

More Related