March, 2009
2
1. (3 marks each; total 9 marks)
Answer each question in the space provided.
You
MUST show your work.
a)
Use Euler’s Method to approximate
)
4
.
0
(
y
with step size
2
.
0
=
h
for the
following initial value problem:
,
'
y
x
y
+
=
1
)
0
(
=
y
b)
A tank contains 1000 L of pure water.
Brine that contains 0.10 kg of salt per liter
of water enters the tank at a rate of 7 L/min.
Brine that contains 0.06 kg of salt
per liter of water enters the tank at a rate of 14 L/min.
The solution is kept
thoroughly mixed and drains from the tank at a rate of 18 L/min.
Set up
the
differential equation describing the rate of change of salt (call it A) in kg in the
tank as a function of time (call it
t
) in minutes,
and
state the corresponding initial
condition. You do
NOT
have to solve the equation.
c)
The reading given by a thermometer calibrated in ice water (actual temperature
C
o
0
) is a random variable with probability density function
⎪
⎩
⎪
⎨
⎧
<
<
−
−
=
otherwise
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 Spring '08
 Mihai
 Calculus, Derivative, Cartesian Coordinate System, Probability theory, Constant of integration

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