What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal...
9. What is the instantaneous rate of change of 2 = f(x,y) = x + xy (with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2) ? e) none of these V13 12 -8 V13 13
10. What is the average rate of change of 2 = f(x, y) = x+ + xy (with respect to horizontal distance) as one travels from (2,1) to (4,-2) ? 12 a) "The o the e) none of these 2 13 b) d) V13
8) a) About how much will f(x,y,z) = xy?z? change if the point (x,y,z) moves from (3.-7.-6) a distance of ds = 0.5 units in the direction of 21 +27 - K? b) Find the maximum change in f(x,y,z) in moving 0.5 units away in any direction, and indicated in what direction this occurs.
Which one of the following is a linear transformation? O F(x, y) = xy O F(x,y) = (22,32) O F(x, y, z) = (x,y – 2,0) O F(x, y, z) = (2,4 – 2,1)
Let f(x,y,z) = xy + z-5,x=r +2s, y = 2r - sec(s), z = s Then I is: ar a. r - sec(s) b. sec(s) c. r+s+sec(s) d. 4r + 4s - sec(s) a. b. C. Given zº – xy + y2 + y2 = 2 and z is a differentiable function in x and y. Then at (1,1,1) is: дх a. 0 b. 1 c. d. e. None of the above o a. o b. ♡ C. o d.
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
which of the following is a potential function for F(x,y,z)= < y2 +y?ex?,x2 + 2ye*?,xy + xy?e *V> f(x,y,z) = xyz + y2exyz f(x,y,z) = xyz + y2e*+2 b. F(x,y,z) has a potential function but it is not one of the other choices. F(x,y,z) does not have a potential function. d. f(x,y,z) = xyz + y2exZ e.
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy 3. Consider the function F(x, y, z) for x, y, z z 0 defined...
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?