Math 20C (Shenk). Summer, 2010. Exam 2.
(10 points per problem. Maximum
=
80
points)
Name
Section
Work alone and use no books, notes, or calculators. Show your work with your answers on 8.5”
×
11”
paper and staple the pages to the exam when you turn them in.
Problem 1
A toy car is traveling counterclockwise around the circle
x
2
+
y
2
= 4 in an
xy
plane with
distances measured in meters. When the car is at (0
,
2), its acceleration vector is
a
= 5
i
−
8
j
meters per
minute
2
. How fast is it traveling and at what rate is it speeding up or slowing down at that time?
Problem 2
Draw and label the level curves
f
= 4
, f
= 6, and
f
= 8 of the linear function
f
(
x, y
) = 2
x
−
y
+ 6. Then draw
∇
f
at one point in the drawing, using the scales on the axes to measure
the components of the vector.
Problem 3
The volume of a right circular cylinder is calculated from measured values of the radius
r
(feet) of its base and its height
h
(feet) with the formula
V
=
πr
2
h
(cubic feet). The radius is measured
to be 3 feet with an error
≤
0
.
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 Spring '08
 Helton
 Math, Calculus, Mathematical analysis, Imperial units

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