Math 1320 sec 004
November 15, 2013
Name: I
‘
( by writing my name I swear by the honor code
Read all of the following information before starting the exam:
• Show all work, clearly and in order, if you want to get full credit. I may take off points if
I cannot see how you arrived at your answer (even if your final answer is correct).
• No calculators/books/notes are allowed for this test.
• Please keep your written answers brief; be clear and to the point. You may lose points for incorrect or irrelevant statements.
• Please turn off celiphones, turn hats backwards, take out headphones and sit every other seat, if possible.
• You have 50 minutes to work on this exam.
• Good luck!
Page (value)
1 (20 points)
2 (15 points)
3 (20 points)
4 (20 points)
Total (75 points)
Score

1.
(O points) Short Answer. For True or False you must write ‘True’ or ‘False’ and justify your answer to receive credit.
s, a.
(4 pts) Consider a 3-d curve (t).
Write down a formula that calculates arc length, as a function of a time-like parameter, t.
b.
(4 pts) Write down a compact binomial series representation for f(x)
=
(1 + fl c.
(4 pts) What are the transformation equations between Cartesian and cylindrical coordinates?
2
A a.
(4 pts) What is the normal vector to the plane 2 + y
—
2z
=
2?
(-
—Th
I-I e.
(4 pts) True or False. The vectors zij
=
+ and ‘ü
=
— — are orthogonal.
I
( ( f

2.
(15 points) a. (8 pts) f(x)
= ln(x).
Calculate the Taylor polynomial of degree 3 about x
=
1 for the function k r
(
-i
2
0
\
_[
2/)
.7
2 b. (9 pts) Write down an equation expressing the relationship between torque (f), force
(F) and distance (f).
= c.
(4 pts) A force
P
=
8i
—
6 + 9 moves an object along a path given by the vector
6 + 2Q + 4. What is the work done by this force?
(6 4

3.
(20 points) a.
(8 pts) and (4,3,10).
Find an equation for a sphere if one of its diameters has endpoints (2, 1,4)
41
-z
R-)
3-
*
-
-
(I x
— b. (12 pts) Find the equation for a line that intersects the planes x + 2y + 3z
=
1 and y + z
=
1. (hint: the point (1,0,0) lies on this line)
—‘ ni:
I
3J
II]
$
‘
-\
— x
II J
I t-
/
0
/
\

4.
(20 points) a.
(3 pts) Consider a curve i(t).
Wrrite down the relationship between the unit tangent vector.
T(t). and the unit normal vector, N(t).
iI b. (7 pts) Find the unit tangent vector to the curve (t)
=
± + (1 + t the point (0,1,0).
3Z r7L 4
:l(6r;
In
{1
I c.
=
(10 pts) A moving particle starts at an initial position (0)
= with initial position
—
+
.
Its acceleration is 3(t)
=
4t’ + 6E +
.
Find its velocity and position at time
S
+
-_)
i
J
1
2
(2)
J a1
L
*
-
3+
4t
/
1

-:44
1’ ‘ •
-k’ 11
‘‘
T 1
-,
.
)
:.
fl.;
A