Fall 2009 Math 151
2
Week in Review X
1.
Setion 4.6
Find the exat values of eah of the
following:
ourtesy: David J. Manuel
(a)
(overing 4.5, 4.6, 4.8)
cos−1
√ !
3
−
2
arcsin(−1)
4
−1
() cot sin
5
3
(d) sin 2 arcsin
5
1−x
−1
Compute lim tan
x→0
2x2
(b)
1
1.
2.
3.
4.
Setion 4.5
Strontium-90 is a radioative isotope
with a half-life of 25 years. If there
are 20 mg of Strontium present, how
muh remains after 15 years? When
will there be only 5 mg left?
2.
3.
Aording to UN data, the world
population at the beginning of 2000
was 6 billion and growing at a rate
of 1.6%. Assuming an exponential
growth model, estimate the world population at the beginning of 2010.
4.
Use
(b)
3
1.
()
(d)
1
f (x) = arcsin
x
1
y = x tan−1 (2x) − ln(1 + 4x2 )
4
t3 − t2 − t + 10
t→−2
t2 + 3t + 2
1 − cos x
lim
x→0
2x2
lim+ x ln x
lim
x→0
lim (1 + e2x )1/x
x→∞
The 4.3 WIR used the
inter ompound
r mt
est formula A = P 1 +
. Find
lim A
m→∞
1
prove
Compute the following limits:
(b)
2.
to
Setion 4.8
(a)
A tank initially ontains 100kg of salt
dissolved in 2000 liters of water. Pure
water enters the tank at a rate of
50 L/min and the mixed solution is
drained from the tank at the same rate.
Find the amount of salt in the tank after t minutes.
funtions
Dierentiate and simplify the following:
(a)
Newton's Law of Cooling states that
the rate of hange in the temperature
of an objet is proportional to the differene in temperature between the objet and its surroundings. A up of
oee with an initial temperature of
90◦ C is in a room that is held at a
onstant temperature of 20◦ C . If the
liquid ools to 75◦ C after 5 minutes,
what will its temperature be after 15
minutes?
inverse
d
1
(tan−1 x) =
dx
1 + x2
m