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Problem #8: Let f(x, y, z) = xzly. Find the value of the following partial derivatives....
Let f(x, y, z)=zxly. Find the value of the following partial derivatives. (a) f(4,4,3) (b) fy(4, 2, 4) (c) f(2,4,3)
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x + y) - 2 cos(x - y). A. SI = fr = B. = fy = c. = f-z = D. = fyy = E. By = fyz = F. = Sxy=
Problem 5. (1 point) Find all the first and second order partial derivatives of f(x,y) 7 sin(2x + y) + 9 cos(x - y). A. = fx(x,y) = B. = fy(x, y) = af C. ar2 = fcz(x, y) = af D. ay2 = fyy(x,y) = E. af деду fyz(x, y) = af F. მყმz = fxy(x, y) = Note: You can earn partial credit on this problem.
For questions 3-8: 5y2 Let f(x, y) = + y 2 Find the two first partial derivatives and the four second partial derivatives of f at the point (1, -2). Question 6 Find fry (1,-2). Question 7 Find fy (1, -2). D Question 8 Find fy: (1, -2).
Find the first partial derivatives of the function. f(x, y) = 2x + 4y + 8 fy 2 fy = 2 X
1.Find the partial derivatives of the function f(x,y)=(8x+8y)/(6x-7y) fx(x,y)= fy(x,y)=
Find fx, fy, and fz 5) f(x, y, z) = ln (xy)?
8. Let Y, Z be uncorrelated with My = uz = 0 and oy = ož = 02, and let X(t) = Zcos(t) + Ysin(t). In class, we showed that X() is WSS. Now let fy = fz where fz is as shown below. Afz(2) 1/2t 1 2 a) Show that My = Uz = 0. b) Find oy = oz. c) Find fx(x;0). d) Find fx(x;). e) Show that X() is not 1st order stationary. Note that you have...
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
Problem 3. Define the function: 2+_ 0 if (z,y)#10.0) if (a,y)-(0,0) f(x, v)= (a) Graph the top portion of the function using Geogebra. Does the function appear to be continuus at 0? (b) Find fz(z, y) and fy(z, y) when (z, y) #10.0) (c) Find f(0,0) and s,(0,0) using the limit definitions of partial derivatives and f,(0,0)-lim rah) - f(O,0) d) Use these limit definitions to show that fay(0,0)--1, while x(0,0)-1 (e) Can we conclude from Clairaut's theorem that()-yr(x,y) for...