13.11.07
CALCULUS II
TEST I
NAME...........................................................................................................
1.(7p) Let z = x2 + 2 y2 - 2 , draw two level curves:
(a) one that passes through the point (1,1)
(b) one that lies on the xy-plane.
2.(7p) Show that the limit
does not exist.
3. (7p) Show that is a solution of the following differential equation
uxy = 4xy u.
4. (7p) Use the chain Rule to find the partial derivatives of
f(x,y) = x ln(x + 2y), x = t2 + s, y = t s
5. (8p) Find all the critical points of f(x,y) = 9xy – x3 – y3.
6. (8p) Find the largest and smallest value of
f(x,y) = x2 - 2y2 - 6x
in the circle .
7. (6p) True or False?
(a) Let f be defined on some neighbourhood of point (0,0) and both of the partial derivatives fx(0,0), fy(0,0) exist, then the function f is continuous ?
(b) If as along every straight line through (a,b), then
.
Phoob