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Unformatted text preview: $617,963“ 5 _
[ MATH 141 E I EXAM II I I SAMPLE B J
x3 — x2 + .7: —1 1 0c
1. Evaluate the Iim ———, 5. Which one of the following is true for the integral f —d.r?
:ml 2x3—x2 —x 2 [I— lip a] E a) Diverges for p = 1 and converges for both go > i and p < I.
j b) Converges for p S 1 and diverges for p b 1. b) 5 c) Converges for p > 1 and diverges for p g 1. C) E d) Converges for p 2 1 and diverges for p < 1. d) 1 e) Converges for p < l and diverges for p 2 1. e} U (l}”{ln(?i)}2
5. Find the limit of the sequence on = ——————. e2”c — 1 n
‘2. Evaluate the lim .
:cmﬂ 23:3 a) 1
2
3) +00 b) e
bl —00 6) —oo
c) 0 d) 0
2 e) +00
d} e—
2
e) cannot be determined 7. Find the sum of the following series:
i“: (—ainl
ln(sin(3x}) “:1 4" 3. E a] t ti 1' —.
v ua e [e $133+ ln(tan(3:.~:}) a) l
a) 3 7
1
b) D b) __
T
c) —d T
c) ——
cl) 1 4
7
: «1 d _
L) ) 4
e} T
1 2dr
4. Evaluate/ —2.
. ..1 x
8. For which values of p is does the following series converge?
a) 0 i 1
b) 2 “:2 ni’lnhrDV—T
L) 2
a) P2 8
d) ——4
b) p) 8
e) does not exist
L) p> 7
d} p< 7
e} :22 7 MATH 1‘11 EXAM II SAMPLE B 9. Which of the following is true for the two series given below: 0‘3 _ n
10_ gm
n=1 "n +3 +00 ,1 DC! In!
(I) 2 (1:11) (H) z n?
n=2 n=1 a} Only (I) converges. 11. Z
":1 3112 _ 6
b) Only (II) converges.
c) Both converge.
. (3:
d) 30‘” dwerg“ 12. Z (—1)"[ln(2n + 1) — lnln + an“
e) None of the above. "*1
00
(‘3)1’1114
13 Z T
nﬁl ’ For problems 10 to 13 (each worth 5 points), determine whether
each series is absoluter convergent, conditionally convergent, or di~
vergent. Be sure to code your scantron sheet as follows: A M if the series is absolutely convergent.
U H if the series is conditionally convergent, D H if the series is divergent. MATH 141 EXAM II SAMPLE 13 _ °° d3: 15. {5 points each) Determine whether the following series are corwer—
14. (10 pomts) Evaluate 2 . .
Wm x + 4 gent Dr divergent. Please be Sure to Show your work. MATH 141 EXAM II 16. (3 points each) Determine whether the following sequences converge
or diverge.
If the sequence converges. find its limit. If the sequence diverges.
circle the word "Diverges" and explain why. a) {4:} Converges to Diverges (justiﬁcation): b) {cos }
Converges to Diverges (justiﬁcation). C) {sinrjinj} Converges to Diverges ustiﬁc atiou ): d} {(HEY} Converges to Diverges {justiﬁcation}: 1n(n)
L} {mam}
Converges to Diverges (justiﬁcation): EXAM lI VERSION A 1. A2. A3. 0%. E5. CB. D7. A8. 139. C10. 011. D
12. A 13. A 14. 5 l5. a.)Ccnverges by ratio 131151. [Show work): b} Converges by root test (ratio also works but more difﬁcult}; 16. a}
converges to D; b} diverges; c) converges to I]; d) converges to 88', e}
converges to 1 SAMPLE B ...
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 Fall '07
 BOMAN,EUGENE
 Math

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