Chapter 15: Suggested exercises

• Sect 15.2: 1bhk, 2b, 3d, 4, 7, 9, 10, 11ab
• Sect 15.3: 1ab, 2, 4, 5, 10ab, 13, 14ae
• Sect 15.4: 3, 4, 6, 8f, 11b,j
• Sect 15.5: 1b, 2, 3, 11b, 12b, 14
• Sect 15.6: 2, 3, 7

extras on 15.2:

• What is the length of the ellipse of major diameter 2 a and minor diameter 2 b ?
• What is the length of the parabola y = x² from x=0 to x=2 ? What is the curvature and center of curvature of that curve at x= 1 ?
• The cycloid is the curve followed by a point on the rim of a wheel rolling along a plane.
  Can you find a parametrization for that curve and calculate the length of the cycloid from the point where it touches the plane to the next such point?

extras on 15.3:

• Calculate the integral over the triangle (0,0), (0,1), (1,1) of the function f(x,y) = x² sin(xy) .
• What is the volume of the wedge of material cut out of the cylinder x² + y² =4 by the planes z² = y ² ?