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Find the derivative of the function at P. in the direction of A. f(x,y.z) =5 e* cos (yz), Po(0,0,0), A=i+2j+ 3k (DAf) (0.0.0) = (Type an exact answer, using radicals as needed.)In what directions is the derivative of f(x,y) = xy + y~ at P(2,7) equal to zero? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. U= (Simplify your answer. Use a comma to separate answers as needed. Type your answer in terms of i and j.) O B. There is no solution.The plane z = Ax + By + C is to be "fitted" to the following points (Xk, yk.Zk): (1, - 1,0), ( - 1,0, - 1), ( - 1,1, - 1), 1 + (0, - 1,0). Find the values of A, B, and C that minimize 2 (AX* + Byk + C- Zx ) ", the sum of the squares of the k = 1 deviations. A B = C = (Simplify your answers.)Find the linearization L(x,y,z) of the function f(x,y,z) = / x + 2 + Z at the points (5,0,0), (7,2,0), and (1,2,2). The linearization of f(x,y,z) at (5,0,0) is L(x,y,2) = (Type an exact answer, using radicals as needed.)Use Taylor's formula to find a quadratic approximation of f(xy) = 3 cos x cosy at the origin. Estimate the error in the approximation if |x| $ 0.16 and ly| = 0.07. Find a quadratic approximation of f(x,y) = 3 cos x cosy at the origin. f(x,y) = 3- N/ - (3x2 + 3y?) The maximum error if |x| $ 0.16 and ly| $ 0.07 is (Round to four decimal places as needed.)