Ernst_Test_3_Fall_2007-1

Ernst_Test_3_Fall_2007-1 - 'i~q1L t Jlv.ev'jtll\t 1...

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0 12'3 I i 'I" Ii I' " /JjD lv NAME . ~ \ ..•. \) 1••• -! ~. ',J DEC. 13, 2007 1. (8 pts.) Evaluate the integral. Use proper notation. = ,/; I ~ -kt~-, 'X L I•••• ~ PM Sl~ ~I I, ~ -"/1Jt\ -l"'/tX1 y.. _, -Ie ) St!-/ (Ol» - 5/1.1 t 2. (10 pts.) Determine if the sequence is convergent or divergent. Find the limit. f -- r e" } a. tell +1 - 5 .- 5
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1-5n 3. (8 pts.) Let all = 3 + 5n a. Determine whether {all} is convergent. = b. Determine whether L all is convergent. 1l=1 CP"nV~YL~t !pic.- ~ ~ ~~/Sh 31 ~ 4. (8 pts.) Find the sum of the geometric series. (Define a and r) 00 211 I~ 11=1 e :b- - e 5. (9 pts) Determine the nth partial sum 5" ' and find the sum 5 , of the series. = 3 L n2 -1 1/=2 2 'S .,.
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\ 6. (24 pts.) Determine whether the series is convergent or divergent. = n a. L 1+n2 11=1 ~ ~ \. cl~ ) . \:)L.•.. d.,. '2) v t 1 -7 yo v-;\w1. 1,,1" ~ L'" (I ~..,."l) ~\.l~?"'c\'"
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Unformatted text preview: 'i~q1L t Jlv.ev'jtll\t 1 \ \ l (}>v" )<.C"" [j L--I b. ~ (-1)" 0/'1+' L C} 11=1 (5 + n) N \-, L -1 b I dT j 9'-.1 E:~(;. . '('" . a I S I f I C OAVe. '<Je. .J-~ <0 I' \' = 1 c. L 3r;; n=l \I n '-/. N ) 7. (16 pts.) Determine whether the series is absolutely convergent, conditionally convergent or divergent. a. :t (-1)" n=1-:: 8 b. f~ n=l e2n i---1'\ I} )() l v T I::.l 'I (PNVC'llG~NT 8. (8 pts.) Find the open interval of convergence and the radius of convergence. :t (x + 4)" n=l n r-I-i-~ j ,LJ ) ! ) 9. (9 pts.) Write a power series representation for the function and determine the interval of convergence. x !(x)=2+x...
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