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Unformatted text preview: Exam Three MATH 122 Winter, 2007 NameSO SU S lug; g Section Show all your work on the exam paper, leginy and in detail, to receive full credit.
No Calculators. There are a total of 105 points on this exam. This exam will be graded out of 100 points; hence, there are ﬁve bonus points on this exam.
3 1. (15 points) Find the exact arc length of the curve y = %x3 over the interval [3 , 8]. 5 /,<6
C \1» $13" (k4 __ f \
L 1 3‘ (5*) '" \Xﬂ “<46
G J?
3/ J
—— Z: L .
W a 3X U:\L+\ ddcé»! 0655.33 0653?“ 2. (15 points) Suppose that a population of bacteria grows exponentially, and it growth is modeled by the equation y = 600e%° where t is in minutes. Find the
average number of bacteria in the ﬁrst two hours. b _
S ._\_~ g; Ag Zhrs =— \1O mm
. Que \9—(3‘ J Cuﬁ 5
o ono\ ' l
om)“ O Page 2 of 7 3. (10 points) Find the work required to compress a spring four ﬁfths of a meter if
the spring has a constant of 500 Nm“. Hint: F(x) = kx. K; Sam \\I /m \: (ﬂ =» Ems? W ‘3 X7, ﬂ w—PBFMM : EBQBXb Page 3 of 7 Soéu '— VK)  &U 4. (10 points each) Evaluate the integrals Note: you do not need to simplify your Ixsm(2;)dx :‘:. " \ACOSX —¥ SCO5X AV.
d0:— dY T. —§<C.OS\A 1 SMX + L
(xv f, 3m u ~ \I a  CD 3X
{WW V t X \\\ 6:5} *5 QVL
U =— \<_\ (>3 5 WWW ,._ WMWWMWW
do —: .L. 435:3 Aye : ‘X VG?) ’ 5* "V 9
X3 \w‘ﬂm‘ww .. W
do _’ éﬁ‘
éN 7— é¥
\/ 2. x Page 4 of 7 5. (10 points each) Evaluate the integrals Note: you do not need to simplify your answers. jJ1+cos0sin9d9 k) <— \+ C038 Sxﬂ—L © an© Jsin30d6 =— J
C S \ _ C0329) §\(\éj U: CoSé ‘éUiSWEéﬁD ’5
,3w®m= ;«v+©
_. 3 M/ﬂ—
._ 2:033 ’ cos 9 T L Page 6 of 7 6. (15 points) Evaluate the integral. Note: you do not need to simplify your answer. 2;: 33:61: “’9‘ :2 K 7—»? + 3x 41. ﬂ
J x (3‘55) (we?)
2* + 3x ' \1. A (3 C
‘—:. ——————~ + ——~ 4’ ——
X (mxw 1) “A *3 “1 ZXL +3» ‘\1 t A»?  A»: vng ~+ th~+1l5y + CY? “ECX Z: AtK‘St—L ﬁ‘L—«i—rﬁSeLﬁ @=~—<;
3 —_ _;\+2\3—3<, a 31' *ZQ’EL
“\13‘GA ‘7 A32. +5cvga /> Ci,"
6"\
'L {vyﬁ\ ﬁx ﬁe;
21 T3 —\Z, w \ Si, S11 — J— Zw * 3w— Page 7 of 7 ...
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 Winter '08
 Falco
 Math, exact arc length, dY T. —§, Sam \\I /m, \ACOSX —¥ SCO5X

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