THE UNIVERSITY OF BRITISH COLUMBIA
Sessional Examinations.April 2005
MATHEMATICS 121
Closed book examination
Time:2 1/2 hours
Calculators are not allowed in this examination
I[21] SHORT ANSWERS QUESTIONS
Each question is worth
3 marks, but not all questions are of equal di
ﬃ
clty. Full marks will be
given for correct answers, but at most one mark will be given for in
correct answers. Simplify your answers as much as possible.
a)
Evaluate
R
(
x
2
+
e
2
x
)
dx.
b)
Find the average value of sin
x
on rthe interval [0
,
π
]
.
c)
Find lim
n
→∞
P
n
j
=1
1
n
sin
2
(
j/n
)
.
d)
Find the general solution
y
=
y
(
x
) of the di
ff
erential equation
y
00
−
2
y
0
+
y
= 0
.
e)
Find the general solution
y
=
y
(
x
) of the di
ff
erential equation
y
00
−
2
y
0
+
y
=
x.
f)
Evaluate
R
∞
0
(1 +
x
)
−
3
dx.
g)
A continuous random variable
X
is exponentially distributed with
a mean of 4. Find the probability that
X
≥
8
.
In Questions IIIX, justify your answers and
show all your work
.
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 Winter '10
 Dr.AlejandroCortas
 Math, Probability theory, 1 j, 0.5m, 000kg

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