Answer(s) submitted:
0
1/2
(correct)
Correct Answers:
0
1/2
49.
(1 pt) Consider the function
f
whose graph is shown
below.
This function is given by
f
(
x
,
y
) =
(
6
xy
x
2
+
y
2
,
(
x
,
y
)
6
= (
0
,
0
)
0
,
(
x
,
y
) = (
0
,
0
)
(a)
Find a formula for the single variable function
f
(
0
,
y
)
.
f
(
0
,
y
) =
What is
f
(
0
,
0
)
for this function?
f
(
0
,
0
) =
Find its limit as
y
→
0:
l´
ım
y
→
0
f
(
0
,
y
) =
(b)
Based on your work in
(a)
, is the single variable function
f
(
0
,
y
)
continuous?
?
(e)
Finally, consider
f
along rays emanating from the origin.
(Notice that this means that y
=
x is a contour of f. Be sure
you can explain why this is.)
15
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Find and simplify
f
on any ray
y
=
mx
.
f
(
x
,
mx
) =
(Again, notice that this means that any ray y
=
mx is a con
tour of f; be sure you can explain why.)
(correct)
(f)
Is
f
(
x
,
y
)
continuous at
(
0
,
0
)
?
?
SOLUTION
50.
(1 pt)
f
u
(
3
,
π
) =
D
u
f
(
3
,
π
) =
759.94
(correct)
51.
(1 pt) Suppose
f
(
x
,
y
) =
p
tan
(
x
)+
y
and
u
is the unit
vector in the direction of
h
0
,
1
i
. Then,
52.
(1 pt) Suppose
f
(
x
,
y
) =
4
x
2
+
y
2
and
u
is the unit vector
in the direction of
h
3
,
2
i
. Then,
(c)
f
u
(
3
,
π
) =
D
u
f
(
3
,
π
) =
16
(correct)
Correct Answers:
<2*y/(xˆ2)*cos(2*y/x),2*x/(xˆ2)*cos(2*y/x)>
<0.349066,0.333333>
0.0111246
54.
(1 pt) View the curve
(
y

x
)
2
+
2
=
xy

3 as a contour
of
f
(
x
,
y
)
.
(a) Use
∇
f
(
2
,
3
)
to find a vector normal to the curve at
(
2
,
3
)
.