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Find the linearization L(x,y) of the function f(x,y) = x" -7xy +7 at P (4,4). Then find an upper bound for the magnitude E of the error in the approximation f(x,y) ~ L(x,y) over the rectangle R: |x - 4| = 0.4, ly - 4| $0.4.Find the linearizations L(x,y,z) of the function f(x,y,z) = 7xy + 8yz + 6xz at (1,1,1), (1,0,0), and (0,0,0).Suppose that T is to be found from the formula T=y (e*+ e "*), where x and y are found to be In 2 and 2 with maximum possible errors of |dx = 0.05 and dy =0.1. Estimate the maximum possible error in the computed value of T. The magnitude of the estimated maximum possible error is (Type an integer or a decimal.)Consider a closed rectangular box with a square base, as shown in the figure. Assume x is measured with an error of at most 0.6% and y is measured with an error of at most 0.70%, so dx we have :0.006 and Idyl V $0.007. X y X lavl a. Use a differential to estimate the relative error V in computing the box's volume V. b. Use a differential to estimate the relative error S in computing the box's surface area S. lavl a. V (Type an integer or a decimal. Round to two decimal places as needed.)Solve by the substitution method. 9x + 4y = - 15 x = 15 - 6y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set of the system is (Simplify your answer. Type an ordered pair.) O B. There are infinitely many solutions. O C. The solution set is the empty set.Complete the ordered triple. Write the solution as an ordered triple. Select the correct choice below and fill in any answer boxes 9x - v+ z = -6 within your choice. 2x + 2y - 3z = 17 x - 3y + 2z = -13 O A. There is one solution, (Type exact answers in simplified form.) O B. The system is dependent. O C. There is no solution.Find the absolute maximum and minimum of the function on the given domain. f(x,y) =3x + 2y- on the closed triangular plate bounded by the lines x = 0, y = 0, y + 2x =2 in the first quadrantFind the absolute maxima and minima of the function on the given domain. T( x,y ) =x +xyty " - 12x + 2 on the rectangular plate 0 s x $9, - 5sys0