Question No. 1:

(a) Find the limits by rewriting the fractions first.

lim(,)(1,1)1228+833

(b) Find x, y, and z ; where (,,)=(2+2+2)

Question No. 2:

(a) Use an appropriate form of the CHAIN RULE to find dw/dt.

(i) w = 5x2y3z4; x = t 2, y = t 3, z = t 5

(ii) w = 5 cos xy sin xz ; x = 1/t , y = t , z = t 3

(b) Use appropriate forms of the chain rule to find z/u and z/v.

z = x/y ; x = 2 cos u, y = 3 sin v

(c ) Let T = x2y xy3 + 2 ; x = r cos, y = r sin. Find T /r and T /

Question No. 3:

(a) Find the derivative of the function at P0 in the direction of u.

(x, y) = 4xy - 3y2 , P0(5, 4), u = 2i + 3j

(b) Find all the local maxima, local minima, and saddle points of the function

(x, y) = x2 +2xy + y2 + 6x - 3y + 5