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April 11, 2006
MATH 200
Name
Page 2 of 9 pages
Marks
[15]
1.
If two resistors of resistance
R
1
and
R
2
are wired in parallel, then the resulting
resistance
R
satisFes the equation
1
R
=
1
R
1
+
1
R
2
.
Use the linear or di±erential
approximation to estimate the change in
R
if
R
1
decreases from 2 to 1
.
9 ohms and
R
2
increases from 8 to 8
.
1ohms
.
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MATH 200
Name
Page 3 of 9 pages
[10]
2.
Assume that the directional derivative of
w
=
f
(
x, y, z
)atapo
int
P
is a maximum
in the direction of the vector 2
i
−
j
+
k
, and the value of the directional derivative in
that direction is 3
√
6.
(a) Find the gradient vector of
w
=
f
(
x, y, z
)at
P
.[5%
]
(b) Find the directional derivative of
w
=
f
(
x, y, z
)at
P
in the direction of the vector
i
+
j
MATH 200
Name
Page 4 of 9 pages
[10]
3.
Use the Second Derivative Test to Fnd all values of the constant
c
for which the
function
z
=
x
2
+
cxy
+
y
2
has a saddle point at (0
,
0).
Continued on page 5
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This note was uploaded on 01/23/2011 for the course MATH 100,200,30 taught by Professor Dr.alejandrocortas during the Winter '10 term at The University of British Columbia.
 Winter '10
 Dr.AlejandroCortas
 Math, Approximation

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