a.

Find the limit by rewriting the fraction first. xy - 3y - 9x + 27 lim x - 3 (x,y)- (3,2) *=3 xy - 3y - 9x + 27 lim x - 3 (Simplify your answer.) (x,y)-(3,2) *= 3Let f(x,y) = x# + y". Find the slope of the line tangent to this surface at the point ( - 1, - 1) and lying in the a. plane x = - 1 b. plane y = - 1. a. The slope of the line tangent to f(x,y) at ( - 1, - 1) and lying in the plane x = - 1 is (Simplify your answer.)dw dw Use the functions below to (a) express dt - as a function of t, both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t. Then (b) evaluate - dt - at the given value of t. w = z - sin xy, x = 4t, y = In (t- 7), z= el-8, t= 8 dw (a) Express dt as a function of t. dw dtConsider the functions z= ?' I In if. x: In [u cos v}: and y = u sinv. dz dz [3] Express E and E as functions of u and V both by using the Chain Rule and by expressing 2 directly in terms of u and it before differentiating. dz 62 11: [b] Evaluate E and E at (usuri 2,3 . E} :32 [a] Find each partial derivative needed to use the Chain Rule to nd 5' j =1 =D D Lrlarl eleele