 # What is the maximum value of xy given that 9x2 + y2 = 9? = 3 1 3...

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What is the maximum value of xy given that 9x2 + y2 = 9? = 3 1 3 4 3 2 Question 2 25 pts What is the maximum value of x + y given that 36x2 + y2 = 36? 135 36 6 1/37 Question 3 25 pts A function f(x,y) subject to a constraint g(x,y) = 0 must always have a maximum. True False Question 4 25 pts What is the purpose of the method of Lagrange multipliers? To constrain a function. To find the relative extrema of a constrained function. To find the solutions to a system of equations. To find the partial derivatives of a constrained function. Question 1 25 pts Calculate the total differential of Z = x2y + xy² + 4x² - 4xy + 4y2 - 30xc + 40y + 104 . (2xy + y2 + 8xc - 4y - 30) da + (x² + 2xy - 4x + 8y + 40) dy (x² + 2xy - 4xc + 8y + 40) da + (2xy + y2 + 8x - 4y - 30) dy (2x + 2y - 4) dz of ( - 2.c - 2y + 4) dz Question 2 25 pts Estimate the value of /864.36 + 1672.81 by using differentials with regard to the function f(x,y) = Hint: 864.36 = (30 - 0.6)2 and 1672.81 = (40 + 0.9)2 50.37 50.36 50.35 50.38 Question 3 25 pts The total differential of a function f(x,y) approximates how much the function changes due to small changes of x and y. True False Question 4 25 pts If the total differential of a function is zero, then the function is constant. True False Question 1 25 pts Compute / 3 / 3 (x² + 2xy+? y2 - 3x + 4y + 2) da dy. -4 -5 2 620 3 1876 3 2464 3 Question 2 25 pts Compute 2 3 (x² + 5xy + y2 + 2.c - 2) da dy. 2 445 12 5 145 24 565 12 Question 3 25 pts If f(x,y) > 0, then / f(x, y) dx dy calculates the volume of the solid R under the graph of f(x,y) over the region R. True False Question 4 25 pts For any function f(x,y) and any a, b, c, and d, poper f(x, y) dx dy = f(x, y) dy dx. True False

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