58.
The sum of the perimeters of an equilateral triangle and a square is 10.
Find the dimensions of the
triangle and the square that produce a minimum total area.
59.
Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart.
They are to be secured by two wires, attached to a single stake, running
from ground level to the top of each post.
How far from the left post
should the stake be placed to use the least wire?
60. A manufacturer makes a metal can in the shape of a cylinder that holds
3
1000cm
of oil.
What radius
and height will minimize the amount of metal in the can?
61. A cylindrical metal container, open at the top, is to have a capacity of
3
24
in
.
The cost of
material used for the bottom of the container is $0.15 per sq. in., and the cost of the material
used for the curved part is $0.05 per sq. in.
Find the dimensions that will minimize the cost
of the material, and find the minimum cost.
Use the figure to find the limit.
62.
3
lim
x
f
x
63.
lim
x
f
x
64.
2
lim
x
f
x
65.
0
lim
x
f
x
66.
lim
x
f
x
67.
5
lim
x
f
x

__________________________________________________________________________________
Find the limit.
68.
2
3
6
3
lim
x
x
x
x
69.
2
0
5
25
lim
x
x
x
70.
0
1
1
lim
x
x
x
71.
2
6
6
3
18
lim
x
x
x
x
72.
3
2
8
2
lim
x
x
x
73.
2
2
3
5
4
1
lim
x
x
x
x
_____________________________________________________________________________________
Find the
slope of the line tangent to the curve
at the point
P
by using the formula:
Slope of tangent line
lim
x
c
f
x
f
c
x
c
.
(You must
know
this formula.)
74.
2
5
4,
(2,
2)
f
x
x
x
P
75.
6,
(3,3)
f
x
x
P
76.
3
2
2
1,
( 2,1)
f
x
x
x
P
77.
2
2
7
3,
( ,
( ))
f
x
x
x
P c f c
78.
Find an equation of a line that is tangent to the curve
3
f
x
x
and is parallel to the line
12
10
0
.

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- Fall '19
- Calculus