Fall 2009 Math 151
(a)
Week in Review XII
(b)
ourtesy: David J. Manuel
()
(overing 5.5, 5.7, and 6.1)
1
1.
2.
3.
4.
5.
6.
2
1.
(d)
Setion 5.5
(e)
A farmer has 1200 feet of fening to enlose a retangular eld bordered by a
river on one side. If no fene is needed
along the river, nd the dimensions of
the eld whih give the largest area.
2.
A retangular box with a square base
and no top has volume V . Find the
dimensions of the box whih minimize
surfae area.
3
A right irular ylinder in insribed
in a right irular one of radius R
and height H . Find the volume of the
largest possible ylinder.
1.
√
f ′ (x) = x − 4 x + 10
1+x
f ′ (x) = √ , f (1) = 0
x
1
f ′ (x) = ex − , f (1) = 0
x
′′
f (x) = 1 + 2 sin x − cos x, f (0) =
3, f ′ (0) = 1
√
3
2
f ′ (x) = x + √ + √
x
1 − x2
A fore with magnitude 20 N ats in
the positive y diretion on an objet
with a mass of 4 kg. The objet
starts at the origin with initial veloity
v(0) = i − j. Find its position funtion
and speed at any time t.
Setion 6.1
Compute
5
X
i2 .
i=1
Find the shortest distane from the
point (0, 4) to the line 2x + 5y = −3.
2.
Compute
20
X
i=1
A movie sreen is 24 feet tall and hangs
6 feet above eye-level. How far away
from the sreen should a person stand
in order to maximize their viewing angle?
3.
Use
of
the
your"
i !
1
2−
2
formulas
on
p367
text
to # ompute
2
n
2i
2X
9− 1+
lim
..
n→∞ n
n
i=1
If a projetile is red from the ground
at an angle θ with initial speed v0 ,
the position of the projetile is given
by r(t) = ((v0 cos θ) t)i + (− 12 gt2 +
(v0 sin θ)t)j. Find the angle whih
maximizes the horizontal range of the
projetile.
Setion 5.7
Find f (x) for eah of the following:
1