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**Unformatted text preview: **WW5
I R;’IATH 141 2 [EXAMII l SAMPLEC‘ 1 F. dl I. . I. l—cosx +oo
' m he "mt $11.11;; I2 ' 5. Find the sum of the series 2 {tan—101+ 1}—tan_1(n)].
Hz!
a) w a) 1r
b) 1
b) E
J 1 4
c _
2 c) E
l 2
d) —- .
‘2 dfr
d _._
) 4 e) r1"he series diverges. 2. Find the limit _1i:nn(1 — mi “’0 a +3
6. If the series 2 an = 10, then ﬁnd Iim ( u n-~+oo 2
a.) 0 “:1
b} 1 a) 0
c} -2 3
b _
"g ) 2
d) r:
13
e) 1n‘2 c) 2
d) ‘2
.1 l
3. Evaluate the integral / —5 dz. 3) 00
. ._1 :12
a) U '3:
7. Determine whether the series is convergent or divergent Z W.
b) l H'.:I
C) ‘1 a} convergent. by the root test.
d) ‘2 b) convergent by the comparison test
3) The integral diVerges- c) divergent by the divergence test d) divergent by the root test +03 n—l
4. Find the sum of the series 2 2 . 6) divergent by the rat-i0 tth
n:1
a) Z 8. For each ofthe series (I) and (II) given below choose the right. answer.
8
+90 2 +oc .
— 1 1 + 3m :1.
8 (I) Z n (M) Z e—H—
b — 4 ‘ 'n I
} .1, “:1 Em. +1 112“ 6
c) 8
2 a) Only (I) converges.
d} :f h) Only (II) converges.
e) 4 (3} Both diverge. .d} Bot-h converge. e} None of the above. +m . . s .
_1 n+1 _ ‘_ t
9. What is the minimum number of terms of the series Z --——( T33 D If It 1" Emerge“
"=1
we need to add to ﬁnd the sum with 1 error I g 0.001?
+30 (-1)“
13. Z
a) 3 “:1 n + 1
b) 5 +00 2
sin n (_l)n
c.) 9 E R)
d) 1] +00 n
' 15. —1 n
e) 1.5 "2:; ) 2 + 1
+00 10. The terms of a series 2 an are deﬁned recursively by equations 15. a] : 1 and ‘l + in n. _ . .
a.“ H = M can. determine whether the series converges or dl- verges. n 17. a) The series converges by the root test. 1)) The series converges by the ratio test. c] The series diverges by the test for divergence.
d) The series diverges by the comparison test. e) The series diverges by the ratio test. +30 22"
II. The series 2 — is l
“:1 n' a) convergent by the ratio test.
h} cmlvergent by the root test.
c) divergent by the integral test.
d} a divergent geometric series. e) divergent by the ratio test. 1
nlnn +"XJ
12. The series 2 {1:2 is a) convergent by the ratio test. b} convergent by the integral test.
e) divergent by the integral test.
d) divergent by the divergence test. e) divergent by the ratio test. For Problems 13- 17, (each worth 3 points) determine whether each
series is absolutely convergent. conditionally convergent. Cir diver—
gent. Code on your acantron sheet: A - if the series is Absolutely convergent, C — if it is Conditionally Convergent, SAMPLE C.‘ MATH 141 EXAM II SAMPLE C 18. {15 points) Determine whether the given sequence converges or 19. [10 pts.) Determine whether the following integral is convergent or diverges‘ If it converges, calculate the limit. If the series diverges circle the answer. 5“
a) a“ = 3n+4
diverges l
b) an = n sin —
Tl. diverges c} an = (—1)""' diverges 4 A
Lil an: diverges RCOSTI. n2 + 1
dive rgee' 6‘.) an 3 i n+1 converges to converges to converges to co 1] verges to (To nve r gas to divergent. If convergent, ﬁnd its value: 1
lnz
—,dx.
f” a Justify each step carefully. a) EXAM Il- FORM A b)1.C‘2.D3.E4.B5.BS.B?.C8.D9.CIU.HII.A
12. 013. 014.1% 15. D16. (31?. A c) 18. a) Diverges; b) Converges to 1: c} converges 1-0 0'. d}
converges to 1‘I e) converges to 0. cl) 19. Converge-5 to —4 {l ...

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- Fall '07
- BOMAN,EUGENE
- Math