Math 151 Week in Review
Monday Nov. 22, 2010
Instructor: Jenn Whitfield
Thanks to Amy Austin for contributing some problems.
All prolbems in this set are copywrited
Section 5.7
For #8 - #12 below, find the most general antiderivative.
8. f (x) = x4 − 9x2 + 2x − 5
Section 5.5
1. Postal regulations specify that a parcel sent
by parcel post have a combined length and
girth of no more that 108 inches. What are
the dimensions of a package with a square
front under the above guidelines which maximize the volume?
1
9. f (x) = 3ex + 4x−1 + √
6 x
3
10. f (x) = sec2 x + √
x
11. f (x) =
7
−3
1 + x2
12. f (x) =
4x10 − 2x4 + 15x2
x3
13. Find f (x) given that f ′′ (x) = 3ex + 5 sin x,
f (0) = 1, f ′ (0) = 2
14. A particle is moving according to the acceleration equation a(t) = cos t + sin t, s(0) =
0, v(0) = 5. Find the position of the particle
at time t.
2. Determine the area of the largest rectangle
that can be inscribed in a circle of radius
4cm.
3. A farmer with 750 feet of fencing wants to
enclose a rectangular area and then divide
it into four pens with fencing parallel to one
side of the rectangle. What is the largest
possible area of the four pens?
4. Determine the point(s) on y = x2 + 1 that
are closest to (0,2).
15. A stone is thrown downward from a building
450 meters high with a speed of 5 meters per
second.
(a) Find the distance of the stone above
the ground at time t.
(b) With what velocity does the stone hit
the ground?
16. A stone was dropped off a cliff and hit the
ground with a speed of 120 ft/sec. What is
the height of the cliff?
Section 6.1
5. A piece of wire 10m long is cut into two
pieces. One piece is bent into a square and
the other into a circle. How should the wire
be cut so that the total area inclosed in a
(a) a maximum? (b) a minimum?
6. A poster is to have an area of 180 square
inches with 1 inch margins at the bottom and sides and a 2-inch margin at the
top. What dimensions will give the largest
printed area?
7. A box with an open top is to be constructed
from a square piece of cardboard, 3 ft. wide,
by cutting out a square from each of the four
corners and bending up the sides. Find the
largest volume that such a box can have.
17. Compute
5
P
i
i=2 i + 1
18. Write in sigma notation:
√
√
√
√
√
(a) 3 + 4 + 5 + 6 + 7
1 1
1
1
(b) 1 − + −
+
4 9 16 25
19. If
4
X
ai
=
1 and
i=1
4
X
4
X
i=1
bi
=
−2 find
(ai + 2bi + 2).
i=1
n
X
n 1
P
n(n + 1)
find lim
20. Given
i=
n→∞ i=1 n
2
i=1
i
n