Fall 2009 Math 151
2. Shifting Funtions Maplet loated at
http://allab.math.tamu.edu/maple/maplets/
Week in Review I
(only works on OAL mahine, Callab
mahine, or any mahine with Maple
ourtesy: David J. Manuel
installed on it)
(overing h 0, Appendix D, and 1.1)
1
3
Setion 0.1
1. Find
the
f (x) =
√
domain
of
the
1. Let
funtion
x+6
.
2
x − 3x − 4
θ
be an angle in a right triangle. If
sin θ =
2x − 3.
2. Find the domain of the funtion
Appendix D
g(x) =
2. Let
θ
sin2 θ =
g(t) = t2 − t + 3. Compute and
expand g(t + h) − g(t).
√
Let f (x) =
x + 1 and g(x) = x2 − 2
. Compute f (g(x)) and g(f (x)) and
cot θ.
nd
be an angle in a right triangle. If
3. Let
4.
1
,
3
3. Given
1
,
3
nd
2
5
cos θ =
tan θ.
4. Sketh
πthe
−3 sin
x
3
at x = 0.
state the domain of eah.
5. A box with a square base and no top
tan2 θ.
and
graph
sin θ < 0,
of
nd
f (x)
=
over two periods starting
has a volume of 40 ubi entimeters.
5. The
Write the surfae area of the box as a
shown below.
funtion of:
a) its width
f (x) = A cos(bx)
Find A and b.
graph of
is
3
b) its height
2
2
1
Setion 0.2
0
1. The graph of
shown below.
f (x) = ax2 + bx + c
Find a,b, and c.
is
−1
−2
−3
−4
−2
0
2
4
sin5 x in the
form sin x P (cos x), where P is a poly-
6. Use identities to write
nomial funtion.
x between
sin x = sin 2x.
7. Find all values of
for whih
1
0 and
2π
4
Setion 1.1
1. Find a vetor whih represents the di-
reted line segment from
B(−4, −1).
Sketh
AB
A(3, 5)
to
and the vetor
in its standard position.
2. Find a unit vetor parallel to the ve-
tor from the point
(5, 2)
to the point
(−1, 3).
a =< 5, 2 > and b = −2i + 4j,
a − b and 3a + 4b.
3. Given
nd
4. Two people are to pull ropes attahed
to a 50 kg box (on a fritionless surfae). The rope to the left of the box
◦
makes an 60 angle with the box and
is pulled with a fore of 6 N. The rope
◦
to the right makes a 45 angle with the
box and is pulled with a fore of 10 N.
Determine how fast the box aelerates
and at what angle from the vertial.
5. (See Figure 11 on p52 for diagram).
A 50-lb weight hangs from two wires.
Find the magnitudes of the tensions in
eah wire.
2