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Unformatted text preview: SAMPLE Math 16C Sec 1 (Malkin) Name: ,
Midterm exam 3 (Sample) Student ID: Mon Dec 1 2008 Signature: ‘ DO NOT TURN OVER THIS PAGE
UNTIL INSTRUCTED TO DO SO! Write your name, student ID, and signature NOW! NO NOTES, CALCULATORS, OR BOOKS ARE ALLOWED.
NO ASSISTANCE FROM CLASSMATES IS ALLOWED. Read directions to each problem carefully. Show all work for full
credit. In most cases, a correct answer with no supporting work
will NOT receive full credit. Be organized and neat, and use notation appropriately. You will be graded on the prOper use of derivative and integral notation. Put units on answers where
appropriate. Please write legiblyH ‘ 
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l SAMPLE 1. (a) Determine the nth term (starting with n = 1) of each of the following sequences:
1. (5 points) 4, 7, 10, 13, 16, 19,22,25, Qw“3ﬂ+\ ii. (5 points) 1, 2, 6, 24, 120, 720, 5040, ahtni  2 4 8 16 32 64 128
111. pomts) —I,§,—'2—7,a,—ﬁ,2—16‘,—m,uu n (21‘
an: ("‘5 ’33:“ (b) (5 points) Determine whether the sequence an 2 gnu—ﬁg converges or diverges. If it converges, What does it converge to? t 1...
09 ﬂ YV‘N“ W
haw M
3. :41
f 2i Y\'¥V\ 2
, mam \  Q) My 5&7bwmce LUMLKFjGA cmci Cami/£664 “he 1— Page 2 of 6 SAMPLE (a) Determine Whether each series conver ges or diverges. You must justify your answer and state which test you are using. 00 2[ Yb!
So am Om : \nSoo new i. (5 points) 2:; “vx
\1 ’— } CL
w , I W Jmééédtireéﬂ (b) (5 points) Find the sum of the series End) (3% + 3.
l“
\ v\ “ LL
)5 CL (jﬂwﬂiﬂt 86KB ' bhx‘fﬁ i‘: ’L>\ HMS QM jimeiric Ere/Lake
R 00 ‘ .Ovm x Zn=0{ “\~ "7;: L A“ U\k\‘ n L:
=§it>VEr3 ﬁLMQ—E—ﬂ
WWW 9% <\ $3??? , . 3nd?
"Vow mm M, M t a» #0.
{y W M Jam #55
2%») v . (b {h 05
: + :3
A10 “‘0 a)“ .I °° ...., 3.,
ﬂ—gﬁﬁszgé “23M avarice
HZO 0°. 3‘? g 57. Zlhw?) 1.: :25. “0 ":LZ: SAMPLE 3. Find the radius of convergence and the interval of convergence of the following power
series. You do NOT need to say What happens at the end points of the interval. (a) (15 points) 22°21 (x _ 1)n' Midwi ‘ HM“ I M , “i
{gigs (Anon (Xvi 7 (in n _ \ “Lf
: Jim i ’ 0‘ "Oi : jam i3 imam“) U" )3 O ‘ vvwo g, Hie moth» Muir—ecch (:3 m
ﬁ/MQ Mil wok/m»? of cm “576%? 4c I"! (~09 00). {P500 vx 1—. )
M 5 H . E,“ ‘n (w)
w 4 / a ’7” )LM : i ' r)—
“a; \\ N“ 5 [ \i/h
V < l \1+\\<§ (:3 A ()u/\ (g (I) L (1411‘ Page 4 of 6 SAMPLE
\ 4. (a) (10 points) Find the Maclaurin series for f = cos(m) by using the fact that = 2:0 (§;i)1")!$2n+1 and %(Sin(w) : cosh»
LL 9 (~ DA hm) : (th (FUNK) f )L K “to (Lun .
00 ($9 V\ ,
1i E'DK LwH («0 A, MM)
1’ (M (amid) : ZO/wm doll 
h:0 Y\~—/O ‘
00 V\
: Z a: \ (ix/w 3L1“ ‘va “31
W70 (1“ 3 M QM! : Ow).
& V (b) (10 points) Approximate the deﬁnite integral fol e“$2dx using the 4th degree Taylor POIynomial for 6"”52 centered at O. Hint: 6‘?” = 20° (1)" 2n
n=0 n! SC . LEA“ Mame/toga @obmmiod :. 1 — 76 Ar 2%,.
\ K V L l (L X + 3“ dine 5“ KOQJM‘A LP
3 Page 5 of 6 SAMPLE 5. (10 points) Suppose that a rubber ball, when dropped on a ﬂat concrete surface,
rebounds 90 percent of the distance it falls. Find the total vertical distance, both up and down, traveled by the ball if it is dropped from a height of 10 feet onto a ﬂat
concrete surface and allowed to bounce up and down freely. u vml\\
(a) Find the total vertical distance, both up and down, traveled by the ball
hitting the ground for the nth time? (b) Find the total vertical distance, both up and down, traveled by the ball if it is
allowed to keep bouncing forever (Le. n —> 00)? 0“ t \0
ml (1L 4m MM 0
~— qs : \O wmxlo drown 0% = lOt Log no i Mﬁtxmi 1.x 09m. D" I k S0) Q“: ﬂ [S QM
h:O (ilx‘ramu headed up amid W W“ \iwmoe ““ t
it w amt: imam 2mm 40 Vvsov V‘f’c’o kw
1C)
90 \L . w
C 2 realm ~\O : \voa ‘0
“’0 L9 y W
Wﬂc 86W“ ' O‘kqgjﬂ’.
ant), v“: M Z \
END OF EXAM Page 6 of 6 ...
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 Spring '08
 Kouba
 Calculus, Power Series, Radius of convergence, total vertical distance

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