____________________
PRACTICE MIDTERM 2
Math 1320 sec 004
November XXX, 2013 Name: 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 iii 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 fiuial 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.
(20 points) Short Answer. For True or False you must write ‘True’ or ‘False’ and justify your answer to receive credit.
a.
(4 pts) Set up but do not evaluate an integral that represents the arc length of the curve segment parameterized by it)
=
/
,
,
L b.
(4 pts) The point P is described in Cartesian coordinates as (0, 1). What is P in spherical coordinates?
r
Cc’-.
-
c.
(4 pts) True or False. The vectors Zj
= l + and ü
=
— are orthogonal.
d.
(4 pts) True or False. The planes 2x + 6y + 3z
=
9 and 4x
— l2y + 6z
=
10 are parallel.
; DLii-)--2,>
0
\LS e. (5 pts) Describe the shape of the curve given by i(t)
= costI + sint + 3t1.
c c cS

4.
(20 points) a. (6 pts) Write down the parametric equations for the line that passes through the points (6,1,.-3) and (2,5).
=
?c
b. (7 pts) Find an equation for the plane that contains the vectors 5j
= i + 2 + 3 and
=2+6.
4-L
-i i
2-
3
\
-
=
C) c( j-
_\
0
) c. (7 pts) Find the angle between the planes x + y + z
=
1 and x
—
2y + 3z
=
1.
I’
= Z )
A
2-
=

c
5.
(20
a.
(10 b.
Calculate the curvature for the curve (t)
=
3t± + 4sint + 4cost.
Find the unit tangent vector to the curvex
= int, y
= z
= t point (0,2,1).
c.
Consider a curve parametrized by x f(t) and y g(t). Write down a formula for the curvature in terms of f and g.
Cct c
[c-b
(=
/
Lsi
A
(k) =
-çt
_(oc/ c ()< (
\ ç\
—
l),
Z5
_\
-1: cs
—
—
L
I
‘
-
)
T
At
41-
I
A