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Unformatted text preview: —— , ' , 6) 12am ~ 2
1. Which of the following is NOT equal to /O x/4 — xgcim? ” 2
. —_ _  2
A. 11151301.; n 4 (21) /n2 B. 7r
C. F(2) — F(O) where F’(:c) = V4  x2 71—1 2
E. Rhino .2 5V4 — (202/712 1 // 7
S Livy” VL" 'L/ ‘// . 2
o l 1.2.” Suppose that the function f is continuous and differentiable on the closed
interval [—1,2]. Assume that f(—1) = —5 and f(2) = 7. Which of the following is
NOT true of the function f? A. f achieves an absolute maximum on the interval [—1, 2].
B. There is a point c in the interval [—1, 2] where f(c) = O.
C. There is a point c in the interval (—1, 2) where f’(c) = 4.
D. The above statements must all be true for f.
@The above statements can all be false for f. gymhich of the following describes the set of real mimb ers on which the function
“33) = ln(l + x2) is concave down? A.O<:I:<1
.113’>1
C.—l<x<l ffny 1 2X
D.x<—1 14 x1
E.$>l I
f (x) —, 1W)": 10’9””)
.911» I+k"
ll
_. f _ )9
W
I I
f\ (/ m f
sins:
4. Evaluate/(cosxﬁ dill LL: WK A' §(COS$)._§+C 56% :  9/4 x M
B. %(cosx)%+C
3 @§(cosx)§+0 Sfﬁx 1X: _. I‘M D. —g(cosx>% + 0 (mm
B. . _2
~§(sm:c 2 + C "5. The difference of two numbers is 20. What is the smallest possible value for the
”product of these two numbers? A. —100 ‘ :10 t” ': ‘
13*240 X3 > a X20
0—400 minimize x3
13.100
E240 Fm”: x1wx
fl“) : 1X—2.a Xz/O ,. ‘l /1__ _
@ztEvaluate lim “in—3:.
f » 1'—*‘8 2+:c5
6—2 ‘_ x 5 3
B. 00 a w i
'2 + X”;
(1—00 X»)»&
D. f4 ‘,
E 8 ' a m 1/44. Z 3 KI/s
Z: “a
K“) '3) J X‘2/‘5 y¢,a7 2 (7K
3
 L
: 3 / __ ' 2
2 3 7 The area of the region lying between the curves y— — 22:»:1:2 and y —
to which of the following? A. 2
B. 9
C. 4
D. 27 wwwwwwwwwwwwwwwwwww 1 @ 9/2 —~:r is equal 1x
3X**’
'5
'5(3XK1>6{X
0 I ’ timest=0andt==313: 0% meters per second . T52 meters per second
C 11411(4) meters per second
D.» —9 meters per second
E. 4— meters per second U,“ : say—3C0)
3 _,’_l 1 2 ‘4 —  “‘ Problems 9 and 10 refer to the graph 3/ 2
means that the function’s value is not the means that the function’s value equals the height of that circle. f(LL‘) depicted above. An open circle
height of that circle. A solid circle 9; The number of values a in the interval [—8, 8] for which lirn f(a:) does not exist is: Al \¢/ 1.
.2 ) I
(3.3
D4 E. 5 or more 3 Kill” f’ is the derivative of f, then f’(a:) < 0 when: A.:z:=——6
B.l<:1:<2
C.:c=4 @sc>6 E. none of the above 11'1'1If ﬂag) 2 e31" — 6‘3“”, then what is the 1271th derivative f<1271)(av)? A. 31271f(33)
B. 638139; __ e—3813m C. 31271f(—CZI)
D. 1271f<1270>(:c) @31271(€3z + e—Bx) 12 The derivative of the function f(t) = 1n(ln(ln t)) is: 1
A.— ,
t ’ L“, i...
3—1— f({"r”6n(w> M Int
1 tln(t)1n(1nt)
1
1n(1n(1n 2%))
1
tln(t)3 D. E. 13. If f(x) = Axum/Wait then what is f’(2)?
A. O B. §(64—11\/1‘1) C. 1 D 2m @12 f'(k) : (KM) c/ 7+/M/)l
f’m ": s {/7 + 6i :11 . 1
14. If f(x) = VHS/“:6: then If(:1:) ~11 < 1% for all :r > N if A.N=—10
B.N=lO.
CNZ—IOO. I 61’”po ’
\I < _ ,( v, _
aN=100 )p(x3 [0 } K) > K0
EN=rla
II
if”) < ‘“ * far) > 3
’0 , I!)
/0\/7+/0<1//7
; mﬁ+l0>qu
V7 >/«7
J7 >m/u /
X > mo A. B D. E ~73?! stem/y + y2 ' yew/y __ y2
my ' er/y — y2
y 2
E _ 2731261731
year/y + y2
xem/yl— y2 . d
15 If (ax/y = :L‘ + y, then What is Fig? $2+xy+y2 :ﬁgﬁ‘A television camera is positioned 4 kilometers from the base of a rocket launch"
ing pad. Suppose that the camera is always aimed at a rocket, and that the rocket
moves straight upward. If 9 is the angle of elevation of the camera, then 6 = 0
when the rocket is on the launch pad, and 6 increases as the rocket rises. (1) Express tan(<9) in terms of the height of the rocket. (ii) What is cos(6’) when the rocket is 3 kilometers off the ground? (iii) If the rocket is rising at 500 meters per second when it is 3 kilometers high, then how fast is 6’ increasing (in radians per second) at that moment? Express your
answer as a fraction in lowest terms. 0L) {am (9’ : .13 9‘}
7 “I
ix, l
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Likm :90007w ‘7 Wﬁ&:§q
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243) :5 J,— ﬁ'“) fly“)
u, 596%? /
9;; 975‘) : l— L :9
10 I 4/ )— 1
1?. Estimate /_1(5:c2 + 1)da: using a Riemann sum with 5 subintervals of equal
length. Use the left endpoints of these subintervals for your sample points. Express
your answer as a fraction in lowest terms. AX: 3:
l—+—+——+—+'l 9 X0 : "
X4 1 '15‘31 : —E_
5" 5’
)(1 "s “I +1"! e ‘ I
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”UN VHN 11 18. To make a doughnut for breakfast, rotate about the y—axis the disk bounded by (x — 7)? + 3/2 = 9, centered at (7,0). Write a deﬁnite integral that gives the
volume of your breakfast. Evaluate the integral (but don’t eat the doughnut) . 12 :19. Let f(:v) = I(x2—9x+15). Find the absolute m values attained by f on the interval [0, 7].
these extrema is attained. aximum and absolute minimum
Determine the m~values Where each of : 3K /y)( HS’ , 3(x1~4x +3’):"5(xez){x~r) m a < 3,“) X : I $‘ X ': :2 13 20 Estimate {3/664 by the method of linear approximation, using the fact that
43 = 64. Be clear about which function you are linearly approximating and what
its linear approximation is. At the end of your calculations, express your ﬁnal
answer as a single number in decimal notation. I 2/ (6(1)’ a :17?
(K) : L X 3 / 64*:sz
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LU): £(LL!) + (6‘!) (X'Wl
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112? 5.737 10 14 21;”"Write an equation for the tangent line to the graph of y 2 xcoswx) When 33 : 3. 3': XWN"(‘$;A(/M}ﬁé¢x+4ﬂig
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W 3 (s 7
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 Fall '08
 MING
 Calculus

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