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In chapter 1, we talked about parametric equations.

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:.

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In chapter 1, we talked about parametric equations.

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  1. 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.

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

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

  4. 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.

  5. Example:

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

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

  8. 3. Divide by dx/dt.

  9. 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.)

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

  11. This curve is: p

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