7.) Given f(x,1,2)=x²e (9²2) find: > SPIED A.) x (x, y, z) B.) fy (x,y,z) c.)...
Find fz, fy and f. for the function f(x, y, z) = z?eyz
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.
Given z = 2 y2 – 3xy , find the slope of the surface at (1,1,-1) in the direction of ū =< 2,3>
Find fx, fy, and fz 5) f(x, y, z) = ln (xy)?
(4) Suppose that the joint density function of X, Y and Z is given by )<y <<< 1 f(x, y, z) = { otherwise. (a) Find the marginal density fz(z) (b) Find the marginalized density fxy(x, y) 72 (c) Find E (2)
9. The linear function f is defined by f(x,y) = (x + 2y, 5x - y). (a) (5 pts) If ū=(-1,2) and 7 =(3, 1), check that fü+v) = f(ū) + f(ū). (b) (10 pts) Find the standard matrix for f.
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)?
,y)-3x2-5xy + y2 find F 3. or the function (x a) f (x, y) b) fy,(xr, y) c) f(x, y) ,y)-3x2-5xy + y2 find F 3. or the function (x a) f (x, y) b) fy,(xr, y) c) f(x, y)
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney, if 0 < x < f(z, y) = otherwise. Find P(X > 1|Y = y)