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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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