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

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Presentation transcript:

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

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.

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

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

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.

Example 2 (page 514):

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

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

3. Divide by dx/dt.

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

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

This curve is: p