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Question 1 16.67 pts What is the maximum value of xy given that 4x~ + yz = 1? O N/ - O O al - O oo | - Question 2 16.67 pts What is the maximum value of x + y given that 36x2 + 12 = 36? O V35 0 6 O V37 O 36 Question 3 16.67 pts Calculate the total differential of z=xy+xy - 5x2 - 6xy - 232+ 17x+2y+16. O ( x2 + 2xy - 6x - 4y + 2) dx + (2xy + 12 - 10x - 6y+ 17) dy O (-2x - 2y + 6) dz O (2xy + 12 - 10x - 6y + 17) dx + (x2 + 2xy - 6x - 4y +2) dy O (2x + 2y - 6) dzQuestion 4 16.67 pts Estimate the value of v846.81 + 1672.81 by using differentials with regard to the function f(x, y) = Vx2+ 12. Hint: 846.81 = (30 - 0.9)2 and 1672.81 = (40 + 0.9)2. O 50.18 O 50.19 O 50.20 O 50.21 Question 5 16.67 pts Compute ( x+ 4xy + y - 4x - 5y + 5) dxdy. O 80 3 O 16 O 442 3 0 4 Question 6 16.67 pts Compute (x2 + 5xy + 12 + 2x - 2) dx dy. O 565 12 O 145 24 O 445 12 0 5