(8 points) Calculate the following line integrals. (a) (4 points) F Fds where F(x, y, z) = (x, y, xy) and c(t) = (cost, sint, t), tЄ [0,π] . (b) (4 points) F. Fds where F(x, y, z) = (√xy, e³, xz) where c(t) = (t², t², t), t = [0, 1] .

3. Find the derivative of the function f(x, y, z) = xy + yz + za at the point (1,-1, 2) in 3i+ 6j - 2k. the direction A = 3

c) Given the scalar function (x, y, z) = x²e¹- y³ + cos2z. 3π 4 Find the directional derivative of p(x, y, z) at the point Q(1,2,) in the direction of a = 2 i-2j+k. Hence, obtain the direction and the value of maximum change of p(x, y, z) at the point Q.

Given f(x, y, z) = x ln(yz), (a) (b) (c) rapidly; compute Duf(1, 2, j), where u = find the derivative of f(x, y, z) at the point (1,2,1) in the direction the function increases most and find an equation of the plane tangent to the surface f(x, y, z) = 0, at the point (1, 2, ½). 17