211-2008&amp;2009-2-M10-April2009(1)

# 211-2008&amp;2009-2-M10-April2009(1) - Kuwait...

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Unformatted text preview: Kuwait University, Department of Mathematics and Computer Science Calculus C (er-211), MidTerIn 1. April 22. 2009 Duration : 94] min Usa of calculators is not allowed. Please Switch off your mobiles. 1. {3+lpts} (a) Show that the sequence _ n! I , 1: tie — E; T nsmlﬁl is Convergent. CH3 {b} Give the deﬁnition of the convergence ofa series E: n... “=0 2. (2+2+2pts]Determine whether the following series converge or diverge, and if one converges ﬁnd its sum OD w 221:. (b) ink—135;? {cl :ln(n2n:1) 3. {3+3ptslTeSt the following series For absolute convergence, cooditiouel convergence or divergence : W 3 (a) Zen“; 1. 11:1 3° " 31114 n g] [by gel] (am-+3) tan (n). 4. {dotleind the power series representation of or) 4 _ 3 + 2: — :2 in were of I — 1‘, and determine its radius of conver ence. P .r E 5. {Bots} Find the Taylor polynomial of degree 3 for file) = sec[z) at :3 = rr/4. I5. (3pts) Answer each of the following by True or Pelee and justify your answer. {a} lim n,1 =1 2:» lim (our =1. 114m Ira-rich {II N (b) If on < 0, V71 2 1 and Zen converges. then Skirts“ converges. 11:]. 31:1 00 CO 1 SDLUr/O/Vﬁ 'ﬂ-szz-Li..-u 4 - M 41 mm '(m)(“) (M)<_7"1 5200.01.49, %<%<u4 +144. HQMQO<5M<1) MA 1:3 HQ, 5934436 Tiava we. have an“ ‘4. =0_ ¢ 1 v n- .M'r ,_ K e" ‘15“1.+ ' ma“; ” “AWL—1:. ""{W‘om'w ‘b‘g‘oT—‘E’L S") éngiag) W W113 45-va. 5 DQﬂ'w'jion— WM ' ' . . rue» LM ’3. W \— M '20 0.. M-” = M—L_.___‘ _4 :-oO;\$e«-uwe @EE—C—z "vi—"=0 M~Da¢ 41‘ +e" Ina-ac . +4 new 71'” [M 1-2»? («if J 0M4 x1 : eon—— l" = a‘mL30, S“), mﬁ~7Zyo~7En2LI Me awkh {Lite/2W. Kaen 6* Lin! x-w—o 9,“ ﬂy ,‘qpex .4: b“ E (-1.11 5%" IL, :1 guamdw'; oeju'eh What azi. aMJ ,kf-% - Svdﬂe’w‘l 5 O ' I‘ - Covwa win bum m (":30 :‘g—l- .' . ‘ ~ I C. We WNle a=a¢ﬂg+6a M14: ‘, \$2,ch \$3q1+‘_-,f.c7k I: ’ZMOL—J “'1 “)+ 'eﬂ‘ Zw'go éhgk'e-‘LLJ H12 oeru‘os wwwya—u magnum; A 1i. 3.» Q. Hal's—~11“ : Dru—Oi (ACT) we a/eaA-(OL ﬂzonIDHl M4“ ‘ ' alt-Paw ' z MM5 1 7-0 ) awn—J {ho/‘22. flit) ‘- 32%: ) who've Mufﬁw . , 1 _ 4— I‘m-50° + , 3 , v [a 3?“): W40 , ﬂame“: f>ﬁ~ Hana 5m‘17‘47‘1 "‘ ‘JeW'Mé M”! ‘3 CAST), Ea“ cmvmfeh. Thu-r) ‘5. an 3—: cW-a‘t'ﬂc'o-xoﬂlg WV‘V‘P‘MI' M M _~ M 3n+ b. M“, : _3___~:_4;_> M1“ 4 J_,_ can.) . Ayn/,6? Roof 78¢" Ark-+3 L 4.“.1-3 oval {+41 iéhwuwﬂl, 71' 1-2;: “I,” “Ml/911F142!) (“A 1.; CBCT’) we z'qu’ 6‘!) Wu; ' Zak t‘q CMW . 2—4 =2" =~>X=1+iu 7'44». we lwwe 3'1 4+: °° et\ 00 4 1% l. ‘12“)=:1-—r+1‘:; ‘7‘? ‘74—; = 2—75“ 2750")» re» trué" " 4 o a ‘X'H‘L. .71“); ﬁt Wag“ C’L‘Vvﬁugz 1'». k=2. ’23ka “a! i“: (Jr/ewe _ a aou‘u: M +44: wan»: \m‘K “a away. ‘2 J_.“_‘.Q— C’s—1)“. O z~¥1 s--= [.422 '“T -’”—§" ~‘ 7%“) 7%” 4i! (“43+ fCZ-f)&_£)z+ #4,)0_%)3,‘ca/w&4%; ‘8“): "2“ hm") f”(*>= 7ecx My. +0225 Mm aeya'zlavh +S’aec3xl‘MX- ’4’) ’ll {MAME-:4 m4! 9&1: =R) wag gluing”; ‘FC%)__G2 ¥V(L;)=ﬁ)\$u(%)= EWL)_F(£)_E11V; 1T 4 5"“ ”' 3—F" “ M —. . ,. _ 4 m" a al.FaJI>L. Qﬁ-4-f‘; "9'1,Dgui— \$1.4)“: 4+4; L—ae, 5' “we 2 \$100M —- 21m = —Zan J ,4, aka unvmﬁd. 71% t 1 1 2:,(‘4Y‘GK 1'4 J Mu/ a: MW“. ("X 1”; WVMW. (Mm ...
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