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Unformatted text preview: 00010 Math 152 Au. ’11 — K. Kwa ' Name:
SO N0056 Signature:
October 6, 2011 Name.nnn:
Exam 1 I Form A, 7 pages General Instructions: 0 V Do all the problems. Answer each part thoroughly. V o ShOW all Of yOur work! Incorrect answers with work shown may receive partial credit but \
unsubstantiated answers will receive NO credit. You do not need to simplify numerical answers, e.g. 3 + «5/5 — 7/6. 0 Calculators are permitted EXCEPT those calculators that have symbolic algebra or calculus
capabilities. In particular , the following calculators and their upgrades are not permitted: TI—89,
TI—92,and TI—NSPIRE CAS. In addition, neither tablets, laptops nor cell phones are permitted. Special Instructions: 0 The EXam Duration is 48 minutes 0 Thisexam consiSts of 5 problems on 6 pages (excluding this cover sheet). Make sure that your
exam paper is not missing any pages before you start. 0 Answers without supporting work will receive no credit. 0 A random sample of graded exams will be xeroxed before being returned. . Good Luck I 00010 1) (15 points) The graph below represents the velocity v(t) at time t in m/ sec of a particle moving in
a straight line during the time interval [0,10], W) with the tick marks on the axes marked off in sec and m/sec respectively. [In case it is not clear: the
graph passes through the points (1, 2), (4, —1) and (6, —1)] t
6 (3.) Use this graph to complete the following table specifying the location $(t) = / v(s)ds of the
v—\ ' . O P particle at time t. L (b) Determine the displacement (i.e. net change in position) of the particle during the time interval {gm 2; F4 (2
xcg)=5 Vét>dt+ \, Walt +3 moat
o 03 4 g ‘
l‘ ' A r
: 4 — 3 + —’ t “if I ll m. 3
l (c) Determine the total (i.e. absolute) distance the particle traveled during the time interval [0,7].
q . c. ijmlolt 2: Li. + 3 —: 1 m (d) What is the particle’s acceleration at time t = 8? I l. M fie?" f 3" r\
}
J
\.~
v 2) (18 points) (a) Express the following sum (—31t 2w) 21r (—37r 4w) 27r
cos ———+— ——+cos —+'—— —+
3 n n 3 n n \ —37r 67r 27r —37r 2n7r 27r
cos —+—— —+...+cos —+— —
3 n n 3 n n Q in the form 2’: _1aih \ 37L
__ ? Cm C ———+.:D.LJTL)
:‘ h , \ v“, ‘ @ (b) Find a deﬁnite integral f: f (2:) da: for which the above sumis a right Riemann sum. ,__~ 27 (MC YCi‘ X) AX ® 0 V“ : I \ J») / m...— L (c) Use (b) to ﬁnd the limit of the above sum as n —_——> 00. If 2’47 ‘. [5‘ A (:I Jr X) . } I i
‘ Cbb ~71er c? 1" »
JO ( ) X C 7 J0 Q
./ I 00010 ‘ 00010 3) (36 points) Find the following integrals. Show your work. (Numerical answers obtained by a
calculator will receive no credit.) ' 8t 2 4: \1
/(a)/(e 2:4) dt “(CU 44) ‘ 0m
u e ELL
/.
Mrezt  g: i l QB«QEUJW Wow ¥
ﬂlLAr—Qeiﬁal‘: _ 2 d M
l _ 'ug
iiz—al‘t :4 ,L Jékmuﬁméu )080
Elm V 7 .2 2 Gig
6445044 _ . 3[? _ j; M
:: gt—L‘EQSJD— 6?ng +L
I4 3
co m nsin x :1: V 1
/(b)/ t(2)l (2 )[d : f U 0‘31 O S0 (H7 : """" /
t 2 CGiCZﬂ (if «1/ _ 7 , J
"7'“ a“ “ :; “:1?ng
l ,l 73%14) 1 a —2g»e + 0%
g C 656 (2%} ”W U Lél‘rdt 5 f '2‘~w G 00010 32344
9 q:32&44 If {‘ w+\4 i dz 0)
ZR: m—Hé 1“ J 5 U M
3 y
a __ l" \4 0M 0
W : 2423/050 .K 371‘ 0+ 7;) k @
I \
é”? ’3 210g? ,_ J...» (M + MJAA [a \v + L J
"" 371 l
.. ,L (51344 + \Mnbﬂve +C
, . f 41.
(d)~_:‘/§f(a:)dxwhere Z 54: __ gai + £90 1522/“!qu +1
I a: ifx$8 I
“H
m ifx28 , Hint: interpret the inte ral as a difference of two areas. The area formula A : 7W2 mi ht be relevant.
a 7 g g N . 921,” 7
: Sigh :2. j:7c‘*7"l7( Jr M] ”9:09), (9%) «» 
rt 3x3 Wﬁﬁﬁ , 00010 _ 4) (15 points) Let
G(w)= xi/9 (3 f(s) 4) ds Suppose that f(15)= 5 and f915 f(s) )ds= 8. Find 0’ (15. LL @355 ’ ' 3’00: wwww 4 «ﬁg» Ms
Wué  —. _ L ,1 1 r’1 i W 55‘3““??“73'33 X @9014} 0“ (9 3‘“ ’4 f‘
, ‘ In»: ‘1
 Lcd’3¥;\>w~:[3345 >'4JW~‘”’5J
“— 226‘ 33%“? «A
r H wi[‘3K§/‘~ 4XC‘é>]
219 33157
: "L. I Q" €07 >
229 5:15;” 00010
[\ﬁwq rm) 5) (16 points) Find the total area enclosed between the graphs of :1: 2 7y2 — y + y3 and a: = y2 +
63/3. Express your answer as a sum of two integrals that do not involve absolute values. DO NOT EVALUATE THE INTEGRALS. 00030 Math 152 Au. ’11 — K. Kwa Name: '
SO N0056 Signature:
October 6, 2011 Namennn:
I Exam 1 Form B, 7 pages General Instructions: 0 Do all theproblems. Answer each part thoroughly. 0 ShOW all Of your world Incorrect answers with work shown may receive partial credit but
unsubstantiated answers will receive NO credit. You do not need to simplify numerical answers, e.g. 3 + ﬂ/5 — 7/6. 0 Calculators are permitted EXCEPT those calculators that have symbolic algebra or calculus
capabilities. In particular , the following calculators and their upgrades are not permitted: TI—89,
TI—92,and TI—NSPIRE GAS. In addition, neither tablets, laptops nor cell phones are permitted. Special Instructions: 0 The Exam Duration is 48 minutes 0 This exam consists of 5 problems on 6 pages (excluding this cover sheet). Make sure that your
exam paper is not missing any pages before you start. 0 Answers without supporting work will receive no credit. 0 A random sample of graded exams will be xeroxed before being returned. . Good Luck ! 1) (15 points) The graph below represents the velocity v(t) at time t in m/sec of a particle moving in
a straight line during the time interval [0,10], 1’(1?) with the tick marks on the axes marked off in sec and m/ sec respectively. [In case it is not clear: the
graph passes through the points (1, —1), (4, 2) and (5, 2)] . t .
6 (a) Use this graph to complete the following table specifying the location a:(t) = / v(s)ds of the
0 particle. at time t. III
III95
0 03 '\ Limit) [3 Ci 5 (b) Determine the displacement (i.e. net Change in position) of the particle during the time interval
[0,8]. F 3 g“ g  xx W8) : gum—1 alt +3 vimole + 3 meat: Q, l . (g/ z ' _% l 6— =24 m v(c) Determine the total( (i e. absolute) distance the particle traveled during[ the time interval [0,7]. 30 ([lweioltléfg — L3 1:”) l g (d) What isthe particle’s acceleration at time t = 8? "" [ All/$241 00030 00030, N/ 2) (18 points) (a) Express the folloWing sum 1 3 1 3
35+ 55+
33+; 33+;
1 3 1 3
9;+..+ 3 a
3 11.
33+; 3+; 4 in the form 2’: _1ai. VI .55. ,
h Zr’ra @ (9+6) [:0 (b) Find a deﬁnite integral fb f (:12) dx for which the above sum is a right Riemann sum. /
X We:
(‘5) LL (c) Use (b) to ﬁnd the limit of the above sum as n —> oo.
1 z“ 6 ‘ 3) (36 points) Find the following integrals. Show your work. (Numerical answers obtained by a. . calculator will receive no credit.) /(a>/ (en—13)2
dt = f (“a 5); ﬂ 00030 u _ m
: 45‘ ué—Zéﬁjt 1M 0M
, {39% 5‘ W 7 
_ . 3
Cit): Egbert =0 34 jﬂx’lﬁaéu 7+ MM?) 0‘“
_ r7 2:. V 3 ,
"4&de = 3— 1’~é9u9‘—IMl + C
5” . 5 0} _ __~
’1‘ ' if; (2; M
9 B .1 L‘lgflt—l%+C
/ (b) / cot(5:c)lnsin(5r)dx : I U glg (O
7 5’
a me
®A=ﬂwigrw ($.26) C iii; —1 Q 00030 Z7 d __, Z4 25 42’ OJ
/(c)/324—13 z — aft—(’3
[L+ (.75 \ 031%
G) 14232443 : v? 71 (2, ®
24— 0H6 {0 ( ‘
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0W:\;17:3a{%® . A 1
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0‘0} 303‘ J 3g ‘ ’5
\l f 2' % Q:
0‘ 2: (L 3%Lt3+z}ﬂai%¢msgl +C 4
N5 0: if v» «G {‘4'} Aiﬁitéi ~6 L
(d)’_6 f($)d33Where i3— gé 3g ‘ .
J 1: ifa:_<_7
. m—{
M ifo? \Q 9—6 V9
(“+69 "A 2_ _
a .Léxé /L(}j1) 00030 ’ 4)’ (15 points) Let 6 ,
C(20): % / (5f(s)—'10)ds v Suppose that f‘(9) = 7 and f: f(s) ds = 5. @019).
1%
‘ X2 _ _ Q 
pmvhd“ (XL101 ~— ~§§ jxﬁhﬂm ~—t 0:} 054’
m9. _ _ q , _
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_ i (~93) ~— «3; 43>”; ‘0“("91
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: g2“? °' 1m 00030 _ ﬁ[email protected] 5) (16 points) Find the total area enclosed between the graphs of :1: — —29y — y + y3 and II}: y2 + 8y3. Express your answer as a sum of two integrals that do not involve absolute values. DO NOT
EVALUATE THE INTEGRALS. ::;\/?%2_‘X) Ugti) 10:8)‘3‘3 WWl ".h
:Cdlo 4%)“l‘: C? 7/ 3’ M“ Mr ”O (.9 19': )3?!
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 Fall '09
 GELINE
 Calculus, Geometry

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