Math 2720: Multiviariable Calculus
Homework #2
Due Friday, January 16
Problem 1 Here is the graph of the function f (x, y) = x2 − y 2 .
(a) Locate and draw the points on the graph over the points (0.5, −0.5)
and (−0.5, 0). Call them A and B, respectively.
(b) Sketch the slices of the graph through A and B in the x-direction
and the y-direction.
(c) On the back of this sheet there is ordinary graph paper. Draw
undistorted straight-on graphs of these slices on the graph paper
— there should be four graphs eventually, but start with the two
slices through A.
(d) Label the points on your graphs corresponding to the points A and
B (as appropriate) on the surface. Determine the slopes of your
graphs at these labelled points.