This preview shows page 1. Sign up to view the full content.
Math 1920, Prelim 1
October 2, 2008, 7:30 PM to 9:00 PM
You are NOT allowed calculators, the text or any other book or notes. SHOW ALL WORK!
Write your name and Lecture/Section number on each booklet you use. You may leave when
you have ﬁnished, but if you have not handed in your exam booklet and left the room by 8:45,
please remain in your seat so as not to disturb others who are still working.
1) a) (7 points) Calculate the distance from (1
,
1
,
1) to the plane with the equation
x
+ 2
y
+ 3
z
= 0
.
b) (7 points) Find the equation of the plane through (0
,
0
,
0)
,
(1
,
1
,
0), and (1
,
2
,
3).
2) (14 points) The position vector of a particle moving in space is given by the vector function
r
(
t
) = (cos
t
)
i
+ 2
t
j
+ (sin
t
)
k
,
where
t
≥
0
.
For each
t
calculate the angle between the velocity vector and acceleration vector.
3) (14 points) The equation
3
x
2
y
+
yz
+
z
ln(2
x

1) = 0
deﬁnes
x
as a function of the two independent variables
y
and
z
. Find the partial derivative
∂x/∂z
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/08/2008 for the course MATH 1920 taught by Professor Pantano during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 PANTANO
 Math, Calculus

Click to edit the document details