b.
How many of these students were infected after four days?
c.
When will 200 of these students be infected?
d.
What is the maximum number of students that will be infected?
Evaluate.
18.
1
3
cos
2
Sin
19.
tan
sec 3
Arc
x
20.
Convert
2
6 cos
0
r
r
into rectangular form.
21.
Sketch the graph of
2
2sin
r
.
22.
Sketch the graph of
1
2cos
r
.

Calculus Maximus
Limits
Page 3 of 4
Find the limit.
23.
3
3
3
lim
27
x
x
x
24.
0
2
2
lim
y
y
y
25.
2
3
3
3
4
lim
5
2
x
x
x
x
x
Use the power rule to find the derivative when needed.
26.
Find the slope of the line tangent to
3
2
( )
3
4
f x
x
x
x
at the point
1,2
.
27.
Find an equation of a line that is tangent to
2
( )
5
g x
x
and is perpendicular to the line
6
7
0
x
y
Use the limit definition of the derivative to find the derivative of each function.
28.
2
( )
1
f x
x
29.
( )
2
1
f x
x

Calculus Maximus
Limits
Page 4 of 4
Write a function, and use your graphing calculator to solve.
Give decimal answers correct to
three
decimal
places.
30.
A container with a square base, vertical sides, and an open top is to be made from 1000
2
ft
of material
(assume no waste.)
Find the dimensions of the container with greatest volume.
31.
A piece of wire 10 m long is cut into two pieces.
One piece is bent into a square, and the other is bent
into an equilateral triangle.
How should the wire be cut so that the total area enclosed is
a.
A maximum?
b.
A minimum?
32.
On the same side of a straight river are two towns, and the townspeople want to build a pumping
station at point
S
.
Find the distance from
S
to Town 1 that will minimize the total length of pipe.

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- Spring '08
- SPAETH
- Calculus, Algebra, Derivative, Calculus Maximus, 19. tan Arc sec