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Unformatted text preview: L'alculus 11, Final h'xam Review You already have a recent review covering exam #4 so this one covers only the material from the ﬁrst three exams.
Please, do not consider this as your only study tool. Make sure you can do all old tests and quizzes. The formula sheet:
that will be available to you on your ﬁnal include the trig/basic integral/series test cheat sheet that you already have and
the sheet that is attached here. If you have any questions regarding the ﬁnal, please feel free to either call me at home 0.
email me. Your ﬁnal exam will have 16 questions worth a total of 10 points each. The points will be distributed approximately 'A
from the material of each of your four exams. The fmal is Worth 150 points so you will have a 10 point bonus possible.
Good luck studying. 1. Find the area of the region bounded by the graphs of f (x) = x3 w 2:: and g(x) = —x 2. Find the area of the region bounded by f (x) = sin 2: and g(x) = cosx for 35 x .<. {7” . 3. Find the volume of the solid formed by revolving the region bounded by the graphs of y = x2 , x = 2 , and y = 1
around the yaxis. 4. Find the volume of the solid formed by revolving the region bounded by the graphs of y z x2 + 4 and y = 0 around the x—axis. 5. Find the volume of the solid formed by revolving the region bounded by the graphs of y = 2‘ , y = 0 , x = 0 , and
x = 1 about the xaxis. 6. Find the volume of the solid formed by revolving the region bounded by the graphs of f (x) 2 2J; , x = 4 , and the
x—axis about the yaxis. 7. Find the arc length of the graph f (x) = — 8% on the interval [8, 16]. 3. Write the deﬁnite integral that represents the area of the surface formed by revolving the graph of f(x) = 25 — x2 on the interval [0, 25] about the yaxis.
9. A force of 8 pounds compresses a spring 3 inches. How much work is done on compressing the spring 6 inches?
10. Find the work done in ﬁlling an upright cylindrical tank of radius 3 feet and height 10 feet with a liquid that weighs 40 pounds per cubic foot. Assume that the liquid is pumped into the tank through a hole in the bottom of the tank.
I 1. Evaluate the following: 2
a. J——r£r1+_cosx b. I——~———dxx c. Jl—w—dxl d. Ixz cosxdx
sinx (Jr—3W" 0 \lIG—Jr2
e. fax sin x05: f. Jinxjdr g. Ishfx cos2 x55: h Isecsxtansxdx
2
i. Icos‘ada j. j—J—ax k. l. Jug—
tl9+x2 x +9 (36—352?
an —3 3x+4 3 _ (it
. dx . ——dx . xdx .
m lxz+4i3—x) n x(x+3) o I8 p I(x+4)2 l —5 2. Find the following limits without the use of a graphing calculator or table. x—rO 2x2 .l'—)00 x3 x—roe x—buo x: x
a. lim 8 l b. lim E c. lirn e" 111x a. lim(l + 3] n ! 2 3. Write the ﬁrst 5 terms of the Sequence whose nth term is on = l
n + . Determine whether the following series converge or diverge. Name all tests used and show work to support yo
answers. If the series is a convergent geometric series, ﬁnd its sum. 11 00 i b ind—2 c w HI—cos[E] d 2—"—
3"i 3" "2 ’1 "=1 Jn3+2n n=1 ":1 nu] 1 °° sinn ‘” n+1” °° 2n1”
e. — f. E g. E 11. E
Inn 3:3 F} n _l 3n+5 "=2 nu] °° (_ l)n+1 . Determine whether the series
In(n + l) is convergent or divergent. If convergent, classify the series as ":1 absolutely convergent or conditionally convergent. . Find the third term of the Taylor polynomial for f (x) = cos x , centered at x =%
. Find the thirddegree Maclaurin polynomial for f (x) : eJr (x~2)" n3” KI
. Determine the interval of convergence of the series E 91:1 "° (2xr . Find the interval of convergence for W ...
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 Spring '12
 PamelaSatterfield

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