ST 552

Calculus on a Computer

Assignment 6 – Implicit Differentiation & Parametric Equations

1. Consider the circle . Find the slope of a tangent two ways:

a. By solving for y, and

b. By implicit differentiation.

c. Evaluate both at some particular point.

2. Repeat exercise 1 for .

3. Use implicit differentiation to find the derivatives of

a. arccos(x)

b. arctan(x)

c. ln(x)

4. Find the derivative of .

5. Find a parametric equation for the ellipse . Find the derivative three ways:

a. Solve for y

b. Implicitly

c. Parametrically.

6. Suppose a reflector is attached to a 26 inch diameter bike wheel, 8 inches from the center. If the bike wheel rolls without slipping, find parametric equations for the position of the reflector. Plot.

7. Repeat exercise 6 with the reflector at different distances from the center.