math231test2yellowsol - ROW& SEAT...

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Unformatted text preview: ROW & SEAT ———————– ——————————————– ————————— Discussion Section Family Name, First Name UIN MATH 231 Section AL1 TEST #2 YELLOW March 24, 2008 Page 1 of 6 INSTRUCTIONS Show ALL work on these pages. You may use the backside of the page if you need more room for your answer. You are allowed 50 MINUTES to complete this test. Calculators are NOT permitted. THIS PART IS FOR EXAMINER’S USE ONLY Question Marks Grade 1 12 2 10 3 6 4 10 5 10 6 12 Total 60 MATH 231 Section AL1 TEST #2 YELLOW page 2 of 6 Problem 1. Determine the limits of the sequences. Justify your answers! [4 marks] (a ) braceleftbigg n 4 + n- 8 4 n 4- n 2 + 10 bracerightbigg ∞ n =1 n 4 + n- 8 4 n 4- n 2 + 10 = 1 + 1 n 3- 8 n 4 4- 1 n 2 + 10 n 4 → 1 4 for n → ∞ Thus the limit of this sequence is 1 4 . [4 marks] (b ) braceleftbigg 1 n 3 sin(3 n 4 ) bracerightbigg ∞ n =1 It holds | sin( x ) | ≤ 1 and so- 1 n 3 ≤ 1 n 3 sin(3 n 4 ) ≤ 1 n 3 . Since lim n →∞ 1 n 3 = 0, we conclude (with the Squeeze Theorem) that the limit of the sequence is 0. [4 marks] (c ) braceleftBig √ 9 n 2 + n- 3 n bracerightBig ∞ n =2 √ 9 n 2 + n- 3 n = ( √ 9 n 2 + n- 3 n )( √ 9 n 2 + n + 3 n ) √ 9 n 2 + n + 3 n = 9 n 2 + n- 9 n 2...
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math231test2yellowsol - ROW& SEAT...

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