Question: Evaluate the surface integral.∫∫S(x2z +y2z) dSS is the hemisphere x2 +y2 + z2 = 9, z ≥ 0.Help is appreciated! I keep getting the answer is 81(pi) butit's not being accepted. Evaluate the surface integral.

Answer to 1.) Find fx, fy, and fz. f(x, y, z) = x2y + y2z + Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Differentiate implicitly to find the first partial derivatives of z. x ln(y) + y2z + z2 = 79 ∂z ∂x = ∂z ∂y = Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

1. For the function f(x,y,z)=x2y+y2z : (a) Compute the gradient vector. (b) Compute the directional derivative of f at the point P(1,2,3) in the direction of v= 2i^−j^+2k^. (c) What is the maximum rate of change of f at point P ? In which direction does this maximum rate of change occur?

Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = x2y + y2z, (2, 7, 9), v = (2, −1, 2) Dvf(2, 7, 9) = Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Answer to Consider F and C below. F(x, y, z) = (y2z + 2xz2)i. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Question: Find the mass of a thin wire running in a straight line from (3,1,2) to (1,2,5), given that the wire's density at (x,y,z) is δ=y2z(g)(m). [That is: Evaluate ∫Cy2zds, where C is the segment from (3,1,2) to (1,2,5).]

S x2z + y2z dS S is the hemisphere x2 + y2 + z2 = 4, z ≥ 0 Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Explain your answer.(a) xz+xey=y2z(b) 2x2+3y2+4z2=1 Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = x2y + y2z, (2, 7, 9), v = 2, −1, 2 Dvf(2, 7, 9) = Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.