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Unformatted text preview: Math 21C (Spring 2005)
Kouba Exam :5 K E Y Please PRINT your name here : Please SIGN your name here : Your Exam ID Number ____________ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY
WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. PLEASE
KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE
EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK
YOU FOR YOUR COOPERATION. 3. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. No notes, books, or classmates may be used as resources for this exam. 5. 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. What you
write down and how you write it are the most important means of your getting a good
score on this exam. Neatness and organization are also important. (5. You have until 9:50 am. sharp to ﬁnish the exam. PLEASE STOP WRITING
IMMEDIATELY when time is called and close your exam. 7. Make sure that you have 5 pages including the cover page. 8. The following may be used on the exam. Tl n+1
(*> / mm: < /(1)+/(2> +~+f(n> < f(1)+ f<x>dx 1 me) /OO men < f(n+1)+f(n+2)+f(N+3)+~ < 00mm: n+1 n, l.) (9 pts. each) Determine whether each of the following series converges 0r diverges. Write clear and complete solutions including the name of the series test that you use and
what your ﬁnal answer is. 00 n+2 M Vl+9~ M l+ TAD; .., B3
a.)Z( > 3 : w/ 37z+5 “A,” 314+; “+00 3+9: '340
M 235% [email protected]@w 71:1 2 4 8 16 32 _ :L _E’>+ﬂ,_§:+ 
b); 9+2? 81+243 ‘ FD 3 ‘7 a7 3
: oz ‘31“) ”322‘ (:3 ~] —~ an“ ~— M @2me
00 5”“ M a _ V\—>oo an“
e.) 2 (2n)! ) V900 m Gm)!
VlLl. CKW)‘
. 5’ _ v m+ I
: goo (at/H»an b ‘ WM :0“ ”ngﬂ
: ﬂaw/r1 QRVH—QJCEMH] 137
14am 2.) (10 pts.) Start at the origin and move 4 units along the positive yaxis. Turn 90
degrees to the right and move 75% of that distance. Turn 90 degrees to the right and
move 75% of that distance. Turn 90 degrees to the right and move 75% of that distance. Continue this process forming a “spiral with square corners.” Determine the ycoordinate
for the point (x, y) where this spiral “ends.” ‘2
3
If)““" :;q(l+(%) %)3PC%:+~> : 21——'——~— : a...” : (9:4 202.56;
l~LZQ a5 a5
0° 1
3. 8 )ts. The alternatin series ~1 "+1 conver es. What should n be so
> < I > g T}; > W g
TL
 1
that the )artial sum ST : —1 1+1 estimates the exact value of the series with iZI
absolute error at most 0.001 ? We M (““0001 WWW .1 769%” {QWl<am+l)MWW l
Vim—3’
: 3?? 97%
W4”? 2 13000/000 a M W J  ———>2 n+3 Z (000 ">
am; ~ 5 0'00‘ 1
n(ln n)2 OO
4.) (10 pts.) The series 2 converges. What should n be so that the partial sum
71:2 7L 1 . . i ‘
Sn —: E . . estimates the exact value of the series With error at most 0.1 .7
z(lnz)2 i=2 vx 2 292/027) The following EXTRA CREDIT PROBLEM is worth 12 points. This problem is OP—
TIONAL. l.) The following series converges. Determine the exact value of this inﬁnite series : l 2Jr 3 4 5 6
l, 3 32 33 34 35 ...
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 Summer '08
 MILTON

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