Calculus III Quiz 4 Fall 2000 10/4/2000

Each problem is worth 5 points, show all work for partial credit.

1. For the curve given by the parametric equations x = t2+t, y = t2-t, find all values of t for which the tangent to the curve is vertical.
 
 

2. Write an integral for the area under one arch of the cycloid with parametric equations x = t - sin t, y = 1 - cos t. The plot below shows the curve for 0  t  6.

 
 

3. Write an integral for the length of one arch of the cycloid with parametric equations x = t - sin t, y = 1 - cos t, as shown in the graph above.