test3 - MATH 10051 Test 3 November 9 2009 1,7 l4[I This...

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Unformatted text preview: MATH 10051? Test 3 November 9, 2009 1 ,7 l4 ' [I This test paper has X questions and total of 30 marks. It cannot be taken from the examination room. Only nonprogrammable calculators are allowed. Duration: 50 Minutes NAME : STUDENT NO : PART I: Multiple Choice Questions. No partial marks. Circle the correct answer. [2] 1. What is lim (ln(3n2 + 4) —- ln(n2)) ? n~oo (aw:3 (b)3 ® (d)0 (6)00 1111 M737???— Cm Met->77“ n ad) n/Bdo oo [2] 2. For What value of r, the sum of the series 271:? is 8 7 (a); (b); (a)? (011‘? (eg- —3 0’3 do , 3, 3 r g 9r ’ fl {en—ll r. ’—“ :3 3 fl r/ "m- ’ , (,2 V ‘7 , - / r -o -. wrymtgfl a- mmwm-,-\fl~-_ni v- 77 7~ 77 nal 77 nél 7 77 77 777777 9 [2] 3 Wh1ch of the following senes ls/are convergent? ’ (1) i575 ' (n) if 515—3 (in) ii (iv) i 7,1; ta) ((1in (P1) (b) (i) only (c) E ' only (d)<ni)on1y .w and (iii) / 7 7 77 7 77 3 I7 2.3...i ~ [2 ] 4. What 18 the sum of the series £7" g‘? ‘9: I 1"; 3/ 4 71:179. (21):: (b)é (dz (9)?— 3‘r 3 4 3 (—1)”n4 [2] 5. The series 2 ”=1 .Converges absolutely (b) Converges conditionally (c) Diverges MATH 1005F Test 3 November 9, 2009 2 PART 11: Long answer questions. Show all your work. [4] 6. Find the limit of the sequence an = {7 2" + 7" . //)< Go: WW?” 'I” , 00m: (27‘0“) . . °° 4713 + 8 [3] 7. Determlne whether or not the serles Z 3 11:? 2n + n converges. Justify your answer. [AV/W ficZfiE-O (D ”A00 $133+” (3233 W 0/1"“ 46"“ Rfl 6—) of w \‘5 CMWf‘ ’3 nfl/ in +0 MATH 1005F Test 3 November 9, 2009 3 1 [3]8. Deetr ermien eerwheth rro rrnotthese iesz converges. Justify your answer. n__2 n 1n n 1" [3] 9. Deter rim ne whe ther rro rnot the serie es 2 2—111” converges. Justify your answer. n=2 7[@ 133 Me die/WW 58“ (D i («0“ (3 WAVE/gent / nL/Nn nfl’ MATH 1005F Test 3 November 9, 2009 4 00 n [3] 10. Determine whether or not the series 2 n3 + converges. Justify your answer @ l n_12n5+9 {5 o __ /+'-—L”‘+"Z: ’L 4/ + /’zn"— an‘flflq’ 20L )0 00 e p/Senw @n 4 J: m4 Z 7%— ‘5 mfg/3m (P:2>/)> 7) h? , (fig Jive OOMVQW‘SO‘?’ 4696/ (D @ ([email protected] i q ,3 also Com/@361) 15. n 0 ”/I a [4] 11. Determine whether or not the series 2 (-1) 3 converges. Justify your answer. Qn: £707.33 1 r)/Qn) :: V/n IL):3/ 3/}??? n6 have )0 f) It O‘LSO/ZMM (1% W mi We mar—#3, .> J @ 00/ '3 I) (1:. ...
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