(c) F(x,y,z) = E(2,3,4,5)
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 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
Questions A and E (b) f(x, y) = 2.2-2y2-6x + 8y + 3 (c) f(z, y)=x2 + 6ry + 2/-6x +10y-2 Constrained Optimization 3. Find the values of r and y that maximize (or minimize) f(x,y) subject to the following constraints (a) f(z, y) = ry, subject to x + 2y = 2 (b) f(z, y)y+4), subject to z+y 8 (c) f(x,y) = x-3y-xy, subject to x + y = 6 (d) f(x, y)-7-y 2, subject to z ty 0...
17. For f(x, y)=e***+y)? of Ox? XZ of 18. For f(x, y, z)= =? y + z oz 19. For f(x, y, z) = cos’ (3x – y’) – x’ tanz, ar ax of = ? 20. For S(x, y) = x cos y + ye", дхду
Find the derivative of f(x, y, z) = (-4x2y, e-4y+32). f'(x, y, z) =
The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...
7.) Given f(x,1,2)=x²e (9²2) find: > SPIED A.) x (x, y, z) B.) fy (x,y,z) c.) fz (x,y,z) D.) Syy (x, y, z) 8.) At the Point P (1,2), find the slope of the function $(x,y) = 7x’y in the direction of ū = 43,47
Consider the function f and region E. f(x, y, z) = y, E = {(x, y, z)| 1 5 x2 +3? 59,0 SyS 1 - x2 - 22; (a) Express the region E in cylindrical coordinates. O E = {(r, 0, 2)Iisrs9,0 SO S 21,0 S 231-23 O E = {(1, 0, 2)| 1 575 3,0 SOST,O SZS 1-12} O E = {(r, 0, 2)Ii Srs 3,0 s E s 2,0 S 25 1 - 2 O E = {(r,...
F(x,y,z)= (y² +e",2xy +z sin y, -cos y) is a gradient vector field. Compute Sc F. dr where C=C UC2, C, is the curve y=x*, z =0 from (0,0,0) to (1,1,0) and C, is the straight line from (1,1,0) to (2,2,3).
F(x, y,z) = (y2 +e", 2xy + z sin y, cos y) is a gradient vector field. Compute Sc F. dr where C=GUC,, C işthe curve y = x^, z = 0 from (0,0,0) to (1,1,0) and C, is the straight line from (1,1,0) to (2,2,3).