Indiana State University Surveying in Mathematics Calculus Problems

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5 calculus problems that needs answers. They are all shown on the photos that I attached. Thank you.

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Question 9
4 pts
Find the maximum value of f(x, y) = 2xy on the ellipse 3×2 + y2 = 3.
9
1
1
3
0 3
13
1
-1
V3
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IC
مجله
25
2
9
E
2
K
M
Question 11
4 pts
Consider the function f(x, y) = x3 – tan(2y) at the point P (1, 0). Which of the
following is/are true?
P. The maximum rate of change of fat P is 10.
Q. f does not change at P in the direction (-3,2).
R. There exists a unit vector û such that Dù f(P) = 2.
OP and R
O P and Q
OR only
O Q and R
O Q only
A
Question 12
4 pts
дz
If z = (x + y)2, where x = ln(2s – t) and y = 2st, find
Әt
s=1
t=1
8
O 16
0 4
O 12
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Z
Question 13
6 pts
Let f(x,y)
1
x2y +3. Find the following:
3
=
1. How many critical points does f have?
(enter a, b, c, d, or e)
a. infinitely many
b. 1
c. 2 d. 3
e. O
2. Find the extreme values of f on the region D.
x² + y² = 27
D
absolute maximum =
A
absolute minimum =
(enter integers or fractions; enter none if no such value exists)
Question 14
6 pts
A contour map for f(x, y) is given below. Determine the sign of the partial derivative at
the points P and Q.
у
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e
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o
UF
FLORIDA
6 pts
Question 14
A contour map for f(x, y) is given below. Determine the sign of the partial derivative at
the points P and Q.
G @ 3個
y у
DOO
DOR
349
Z
?
X
-2
1
-1 +
W
1.
af
(P)
[ Select]
0
მყ
2.
af
(Q)
дх
[ Select]
0
Question 15
6 pts
Let f(x, y) = (3×2 – 2y2.
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K
N

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Tags:
Surveying in mathematics

mathematics knowledge

surveying mathematics

Mathematical elements

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