2 09/11 F

1. 1st Ed: p54, q47, 2nd Ed: p65, q47. (9 points)

2. 1st Ed: p78, q46, 2nd Ed: p91, q46. $r=\sqrt{x^2+y^2+z^2}$

3. 1st Ed: p78, q54, 2nd Ed: p92, q54. You may want to refresh your memory on total derivatives.

4. The height of the ground above sea level is $\sin(x)\sin(2y)$.
   1. Draw the contour lines.
   2. Consider the point $x=0.5$ and $y=1.5$. Find the gradient of height at that point and draw it in the graph.
   3. If I want to climb to the nearest peak in the shortest possible distance, in which direction should I move at that point? In particular, what is ${\rm d}y/{\rm d}x$?
   4. If I am traveling along the line $y=3 x$ with speed 60, how rapidly am I changing height?