17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find...
The directional derivative of the function f(x, y) = 2x In(y) in the direction v =< 0,1 > at the point (1,1) is equal to 2. Select one: O True False
F(x,y,z) =< P, Q, R >=< xz, yz, 2z2 > S: Bounded by z = 1 – x2 - y2 and z = 0) Flux =SS F ñds S (8a) Find the Flux of the vector field F through this closed surface.
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz, z- xy > and scalar function f(x, y, z) = xy3e2z. Find the following, or explain why it is impossible: a) gradF (also denoted VF) b) divF (also denoted .F) c) curl(f) (also denoted xf) d) curl(gradf) (also denoted V x (0f) e) div(curlF) (also denoted 7. (V x F))
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
Question 10 Compute the flux of the vector fields F(x, y, z) =< x, y2,1 > across the portion of the plane r+y+z=1 on the first octant, with orientation pointing toward the positive x direction. (Do not use Stokes' theorem)
6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at 6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at
cense. This license can only be 5. Given f (x,y) = 12 + x2 + 2y2 the point P(2,1)and vector u =< a. Find the directional derivative at the point in the direction of u b. Find the Gradiant
Problem 1. (10 points) For S(x, y, z) = 2 sin(+ 3) + - yz and P = (-1,0,1), do the following: (a) Calculate the unit vector in the direction of fastest increase of a P. (b) Calculate the directional derivative or in the direction of (2.2.1) at P
9. If f(x, y, z) = x sin yz. (a) (2 points) Find the gradient off (b) (3 points) Find the directional derivative off at (1, 3, 0) in the direction of v= i +2j – k.