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test4 - MATH 1005F Test 4 1 This test paper has yfquestions...

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Unformatted text preview: MATH 1005F Test 4 November 23, 2009 1 ;. This test paper has yfquestions and total of 30 marks. It cannot be taken from the examina— tion room. Only nonprogrammable calculators are allowed. Duration: 50 Minutes. NAME : STUDENT NO : PART I: Multiple Choice Questions. No partial marks. Circle the correct answer. (—1)” 5” n? :13 . n3 [3] 1. What is the radius of convergence of the power series 2 nzl <a>o .§ (as (d); <e>oo 5n+1 n3 .«: SQJ—waas‘ W4”) {:1 fl ‘+ i / g I’? n’f‘i ‘ o, n C“ 1‘ I K —— "E 00 n2 [3] 2. What is the radius of convergence of the power series 2 11:" 7 2" n! 1 :1 (b) 5 (c) 2 (d) 1 (e) 0 '2, 00+} MIL, ‘, 3:21.. .. .filflfil‘kw) on 2” (Mi), 0 .. 0.0 [3] 3. You are given that the radius of convergence of the power series 2 W ' IS 1. _ 37L + 1 71—1 W hat is the interval Of convergence? (a)(*1,1) (1)) [2,4) (C) (3,5) .(3i5l (6) [3,5] iris/3 (70/1,, INA/.4 IFS 0“ n “ Z M 2’: 3., ZN ("1 , W are * X1 .. 30,“ h?! n4! £ r "\ Vrf€n ‘ .70 tin with '3 (”n 95 /§9 ZL/ I X’ " 3n+l MATH 1005F Test 4 November 23, 2mg 2 PART II: Long answer questions. Show all your work. [3] 4. Find the radius of convergence and the interval of convergence of the power series farl)". n21 AN 1 A do @ fl [XV—J n -; "fl/:7”, I); 0 K04 >/\ OW v7 er » 5[5]. Find the radius of convergence and the interval of convergence of the power series C13 2%(I—1Yl' r) wafi—»%W MIL¢%U% n ‘/ 3 fl n i if om 4m [MATH 1005]? Test 4 November 23, 20097 3 [7] 6. Find the radius of convergence and the interval of convergence of the power series i<$n+7f)n' fl ”:1 fl 9") 2; 7+!) J’— ) 9111)-] : "1"”: ’ I Om 1 h :L“ Q” (n+1) ?n I ’3 ,3+}:Q ../5-?:»/0 n 70 f n fljanweygofi IC Zk’gf ; n @359 X" ‘ n?” no |MATH 1005F Test 4 November 23, 2009 4 7. Find a. power series representation for the following functions: [31(a) f(:v)= 3i méi' \Y/e, Lnow M 3 2740) IX “‘59 ap/H , n 3H4 0p 1) 3n” _' X X ZN) X ’ Z( ) 35,, ” mo ...
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