Fall 2009 Math 151
2
1.
Week in Review II
ourtesy: David J. Manuel
2.
(overing 1.2, 1.3 and 2.2)
1
1.
2.
Setion 1.2
Find a · b if a = < 1, −1 > and b =
i + 2j.
3.
Find a · b for the gure below, given u
is a unit vetor
4.
b
5.
a
6.
u
3.
4.
5.
Find the angle between the vetors <
3, 1 > and −2i + 4j.
Setion 1.3
Find the Cartesian equation√ of the
urve parametrized by x = t, y =
2t + 4 and sketh the graph.
Given r(t) = (t1/2 + 1)i + t3/2 j:
a) Find r(1) and r(t + h)
b) When (if at all) does the graph pass
through the point (3, 8)?
) Eliminate the parameter and sketh
the graph.
Desribe the motion of a partile whose
position is given by x = −4 cos t, y =
3 sin t.
Find vetor and parametri equations
of the line passing through the points
(−4, 2) and (2, 14).
Determine whether the lines r1(t) =
(3 − 4t)i + (4 + 3t)j and r2 (t) = (2 −
5t)i + (5 − 3t)j are parallel, perpendiular, or neither. If not parallel, nd
their point of intersetion.
A water balloon is thrown with initial veloity of 15 meters per seond
at an angle of elevation of 30◦ . Soon
you will be able to derive the following parametri equations for√the mo-
Find x suh that the vetors xi + j and
(4 + x)i + 3j are orthogonal.
tion of the balloon: x =
Given a =< 4, 5 > and b =< 1, −2 >
nd the salar and vetor projetions
of:
a) b onto a
b) a onto b
the balloon will strike the ground and
nd the Cartesian equation for the balloon's motion.
15
t − 4.9t2 . Determine how far away
2
7.
6. A 10-kg blok slides down a ramp whih is
5m tall and 8m long. Find the work done by
gravity if the blok slides (frition-free) all the
way down the ramp.
7. Find the distane from the point
line
(1, 5)
15 3
t, y =
2
to the
2x − 3y = 12.
1
How, if at all, does the graph of the
funtion r(t) = ti + (t − 1)3 j dier from
the graph of #2?
3
1.
Setion 2.2
Use axomputational devie to estimate
2 −1
lim
.
x→0
2.
3.
4.
x
x2 + 1
Determine lim
or show the limit
x→1 x − 1
Does Not Exist.
x2 + 1
Determine lim
or show the
x→3 (x − 3)2
limit Does Not Exist.
Find the vertial asymptotes of f (x) =
x2 − 4
.
(x − 1)(x − 2)(x − 3)(x − 4)
2