Question 1: Express as a function of t and find its value at a given value of t w = xey + y sinz -cosz, x = 2vt, y = t-1+Int, z= nt; t =1 Question 2: Find the directional derivative of f(x,y,z)=x yz + 4xzz at P(1,-2,-1) in the direction of vector 2i+j-2k. Also find the maximum rate of change at the given point and the direction in which it occurs Question 3 Show that the given limit does not exist lim xy cos y (x.y) -(0,0) x2 + y4 xy lim (x.y)-(0,0) x10 + y2 Question 4 I ar and - if w=sin(2x-y), x=r+sin s, y=rs at (r,s)=(it,0) - Question 5 Assuming that the equation zy +z3 +y3 - xy- 2=0 defines z implicitly as a differentiable function of x and y, find the value of an oZ at the point (1, 1, 1) Question 6 Find the following limits esin x lim (x,y)-(0,0) X lim cos xy (x.y) -(7,73)