MATH 21A Midterm: MATH 21A Harvard 21a Spring 09Midterm2 Practice2
Document Summary
You do not need to justify your answers in this part of the exam. If the function y = f (x) satis es the relation x2y x + sin y = 3, then what is dy y)? dx (in terms of x and (a) (d) (g) (j) 2 the directional derivative duf (1, 0) of the function f (x, y) = xe xy at the point (1, 0), in the direction of the unit vector u = h 3. 3 on the closed rectangular region with vertices (0, 0), (2, 0), (0, 2), (2, 2), the function f (x, y) = 4 what is the value of the integral z 1. 4 (a) (e 1) (d) 2(e 1) 2 (b) (e 1) (e) 4(e 1) (c) e 1 (f) none of the above. 5 match the integrals with those obtained by changing the order of integration.
