Math 206A Quiz 03 page 1 02/04/2011 Name
1. Consider the function f(x, y) = y−x3
x.
1a. On the blank grid to the right, make careful sketches of the
level curves for this function corresponding to the three values c=
−2, 0, and 2. Label which curve is which.
1b. Explain why lim
(x,y)→(0,0) f(x, y) does not exist.
2. Let f(t) = −−−−−−−→
(t2,cos 5t) and let g(t) = −−−−−−→
(4t3, e3t).
2A. Find and simplify the formula for (f·g)(t).
2B. Find d(f·g)(t)/ dt directly, from your answer to 2A.
2C. In terms of f,gand their derivatives, what is the “product rule” for d(f·g)(t)/ dt?
2D. Verify the product rule “works” in this example, by using it to find d(f·g)(t)/ dt and verifying that you get the same
as in (2B). Show all your steps.
3. Find the POSTFIX-equivalent for the expression ( sin(Y2) + 4X)√XY + 5
