1. Parametric Functions
10.1
Greg Kelly, Hanford High School, Richland, Washington

2. 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.

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

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

5. 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.

6. Example 2 (page 514):

7. Example 2 (page 514):
Find the first derivative (dy/dx).

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

9. 3. Divide by dx/dt.

10. The equation for the length of a parametrized curve is similar to our previous “length of curve” equation:

11. Likewise, the equations for the surface area of a parametrized curve are similar to our previous “surface area” equations:

12. This curve is: p