Math151OldSols3

# Math151OldSols3 - QUIZ ON SECTIONS 11.1-5 SOLUTIONS MATH...

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QUIZ ON SECTIONS 11.1-5 SOLUTIONS MATH 151 – SPRING 2003 – KUNIYUKI 102 POINTS TOTAL, BUT 100 POINTS = 100% 1) Find the limits. Write or -• when appropriate. If a limit does not exist, and and are inappropriate, write “DNE” (Does Not Exist). You do not have to show work. (9 points total; 3 points each) a) lim n n a Æ• , where a n n n n = + Ê Ë Á ˆ ¯ ˜ 1 lim lim n n n n n nn + Ê Ë Á ˆ ¯ ˜ =+ Ê Ë Á ˆ ¯ ˜ = 1 1 1 e b) lim n n a , where a n n =- Ê Ë Á ˆ ¯ ˜ 6 2 5 lim n n - Ê Ë Á ˆ ¯ ˜ = 6 2 5 0 ; we have a geometric sequence for which r =< 2 5 1. c) lim n n a , where a n n n = sin 2 lim sin n n n = 2 0 , by the Squeeze/Sandwich Theorem: 01 2 0 2 0 0 ££ Æ Æ Æ sin sin n n n 123 41 2 3 So, 2) Find the sum of the series 3 4 1 1 n n n + = Â . (8 points) 3 4 3 3 4 3 3 4 1 11 1 n n n n n n n n + = = = ÂÂ Â = Ê Ë Á ˆ ¯ ˜ = Ê Ë Á ˆ ¯ ˜

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Method 1 The first term, a , is a 1 1 3 3 4 9 4 = Ê Ë Á ˆ ¯ ˜ = . The common ratio is r = 3 4 . Sum == - = - S a r 1 9 4 1 3 4 9 4 1 4 9 . Method 2 3 3 4 3 3 4 3 4 9 4 3 4 9 4 3 4 1 1 1 1 1 1 1 Ê Ë Á ˆ ¯ ˜ = Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ = Ê Ë Á ˆ ¯ ˜ = = - = - = - = ÂÂ Â Â n n n n n n n n ar a r , where , and Again, Sum - = - S a r 1 9 4 1 3 4 9 4 1 4 9 3) The series - () - = Â 1 1 1 3 1 n n n is approximated by S 3 . According to our discussion in class, what is an upper bound on error for this approximation? (4 points) - () =- + - + - = = = = Â 1 1 1 1 8 1 27 1 64 1 3 1 3 4 n n n n a S a { 12 43 4 { ... error 1 neglected term st £= = a 4 1 64 Note: S S ª ª ªª 0 9015 0 9120 0 0105 1 64 0 0156 3 . . .. . error , which is less than [or equal to]
4) For each of the following series, box in “Absolutely Convergent,” “Conditionally Convergent,” or “Divergent,” as appropriate. You do not have to

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## This note was uploaded on 09/08/2011 for the course MATH 151 taught by Professor Bray during the Spring '07 term at Mesa CC.

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Math151OldSols3 - QUIZ ON SECTIONS 11.1-5 SOLUTIONS MATH...

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