This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ﬁcZﬁEO (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:. ...
View
Full Document
 Spring '11
 duke

Click to edit the document details