1.) Let f(x, y, z) = xy?z3 – sin(xy) +erz? – tan(y, 3. Determine the following....
pi over 2 is not correct either Let F(x, y, z) = z tan-(y2)i + z3 In(x2 + 2)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 5 that lies above the plane z = 4 and is oriented upward.
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
7. Let z x+y (a) Show that f(z) z3 is analytic. 4 marks Recall the Caucy-Riemann equations are: ди ди an d_ where f (z) -u(x, y) + iv(x, y). (b) Let x2 and y 1 such that z-2i is a solution to 2abi [3 marks] Determine a and b (c) Find all other solutions of 23-a + bi in polar form correct to 2 significant 3 marks] figures If you were not able to solve for a and b...
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...
Q6 [10+1+3=14 Marks] Let F be a force field given by F(x, y) = y2 sin(xy?) i + 2xy sin(xy?)j. (a) Show that F. dr is exact by finding a potential function f. (b) Is I = S, y2 sin(xy2) dx + 2xy sin(xy?) dy independent of path C? Justify your answer. (c) Use I to find the work done by the force field F that moves a body along any curve from (0,0) to (5,1).
Let F(x, y, z) = x2y3 + y 2 sin(π z) /π + z2ex-1 a) Find the equation of the tangent plane to the graph of the function z = z(x, y) at the point (x, y) = (1, 1), if z satisfies the equation F(x, y, z) = 2 with z(1, 1) = 1. b) At the point P(1, 1, 1), determine in which of the two directions ~u = h−4, 3, 0i or ~v = h−3, 0, 4i...
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
3. Find lim f(,y) if it exists, and determine if f is continuous at (0,0. (x,y)--(0,0) (a) f(1,y) = (b) f(x,y) = { 0 1-y if(x, y) + (0,0) if(x,y) = (0,0) 4. Find y (a) 3.c- 5xy + tan xy = 0. (b) In y + sin(x - y) = 1.
1. 2. (1 point) Let f(x,y,z) = 4x2 + xy + yz +5z?. Find the linearization L(x, y, z) of f(x,y,z) at the point (-1, -3, -1). L(x,y,z) = -5x-2y+72-3 Find an upper bound for the magnitude El of the error in the approximation f(x, y, z) ~ L(x, y, z) over the box |x +11 30.04, \y +31 < 0.04, 12 +11 30.04. E 3 (1 point) Let f(x, y) = 3 In(x) +2 In(y). Find the linearization L(av)...