1 / 17

10.1 Parametric functions

Photo by Vickie Kelly, 2008. Greg Kelly, Hanford High School, Richland, Washington. 10.1 Parametric functions. Mark Twain’s Boyhood Home Hannibal, Missouri. Photo by Vickie Kelly, 2008. Greg Kelly, Hanford High School, Richland, Washington. Mark Twain’s Home Hartford, Connecticut.

onawa
Download Presentation

10.1 Parametric functions

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. Photo by Vickie Kelly, 2008 Greg Kelly, Hanford High School, Richland, Washington 10.1 Parametric functions Mark Twain’s Boyhood Home Hannibal, Missouri

  2. Photo by Vickie Kelly, 2008 Greg Kelly, Hanford High School, Richland, Washington Mark Twain’s Home Hartford, Connecticut

  3. In chapter 1, we talked about parametric equations. Parametric equations can be used to describe motion that is not a function. If f and g have derivatives at t, then the parametrized curve also has a derivative at t.

  4. The formula for finding the slope of a parametrized curve is: This makes sense if we think about canceling dt.

  5. The formula for finding the slope of a parametrized curve is: We assume that the denominator is not zero.

  6. To find the second derivative of a parametrized curve, we find the derivative of the first derivative: • Find the first derivative (dy/dx). 2. Find the derivative of dy/dx with respect to t. 3. Divide by dx/dt.

  7. Example:

  8. Example: • Find the first derivative (dy/dx).

  9. 2. Find the derivative of dy/dx with respect to t. Quotient Rule

  10. 3. Divide by dx/dt.

  11. Example 2. Find

  12. Topic 2 • Arc length of parameterized curve

  13. The equation for the length of a parametrized curve is similar to our previous “length of curve” equation: (Notice the use of the Pythagorean Theorem.)

  14. Example: 1 arc length • Find the arc length of

  15. Solution.

  16. Classwork/Homework: • Page 535 (7-16,23-33)

More Related