test1solns

# test1solns - M408D AP-Honors Max score = 100 Circle...

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Unformatted text preview: M408D AP-Honors Max score = 100 Circle discussion group: 8:30 1:00 Test 1 2:00 ESP 9/30/09 Keg Name - Printed Show your work in the space provided except for problem 7. Circle your answers. No cell phones, calculators, etc. are permitted. 1. Find the limit, if it exists. Your answer should be numeric. 71—?OO (6) - “Ob 3‘) 11m xl/glnx Film (} Ich‘l'MMI/xq‘lt O {/3 ac—>0+ I \ (6)—/ A LN. Jaw =/,m ,3x xaa X mo 3 / er+ﬁmm ‘v‘lc 0 ‘ 00 b) lim (tan”1n—Z)n form Is It” I l ‘6) W 2 v' w UH 7:? ,. J: .— / +4,“ V‘“ _'_ llm ’ [m 1+“ A IN ______..-———-‘—‘\ _,__ ’\ 2— kg 00 /n n") 00 n h->ao -l l 2- m = 0) lim sin_1( 4” 1171+“ (/0 Z 7‘ 8112 + 27713/2 + n —— 6 >:. 2. Find, if convergent, /00 \$35954 day 2: //m I X C 90" 1 .6900 l K7 be an de M J— ,. (6) 3 f‘x‘f ___ _ i {e u = _, a!- C 2 ’L/ 6 X G 32" ' I7 ‘1 H {T “X UL: 'xk’ 3 ID : /,M ff;- (3 )l A? R“ 1 A?“ K fad) ‘1 I i 09 : Xsﬁx J. ’f+ “L g : tﬁoo 3. Find the sum of the series, if convergent. -o 4 ﬂan) a>Zln(1+%-) = : ﬁn U—ﬂ — Z («a V‘ n22 “:2. K52. g» It — 3 (6); :[email protected] m. ﬂankgplimﬂﬂﬂ ) Ii h=z 71 , +é€nﬂn+lrzguﬁ):£nﬁ4a’ﬂqz 0‘ 3 b) :3"(7r+1)_" , i (3;; n=4 h: (6) No“) i. 11TH \ \ L ’3 > , i — TH: Tr+| TTH ‘1 TN: 3 Ono—3 4. Classify as AC / CC / DIV. Remember to show your work / give your reasoning. I a) i<3naz+i> : " CMU“)L_( 9) r~ahv 7Lt_(+ n .’ ‘ I ‘L L LCT 0.10% E: 7,“, (6) :ZBIZ QM 5 DD TR I ‘7‘: CMV 4‘9 éQtV.(0’I/€J /1 L(/ e mm b a I" %/_S p\\/ 3 °° <1 >3 1 w. :0 r3 Wax/Ma, b) 2“1)"5372 3‘ w 11:2 m w v\ 3 roe/w M, v\ QM“? InV7 \_]/_ _Fm Amy n M") 3/L \ 4 b/z : 5/7 W m m C T ﬂu _‘/— Cm“ by f'J“/u+q7L‘ f0 - \ S/y/ v\ fox H; IL @ 0° el/n2 L C) EH)" n 6);, , n21 (In (C _/——~ 0. ’14“; (64/61 WW l"D ﬂ‘ m V V1. (6) A i A!” Z )(_\)n e/V:\ A“; L; LCTwnLA in lo 4/?“ “Mu-bx I; @ 7-4 6. Find the interval of convergence. 1-“ I X I a) iewﬁ we «Hack Elk‘fé’? 12"?“ m l 2h+l I)” I “Hi Mil OM?)€ W BL— - If “()0 __ Ln I T Lm+‘)l n z “ (X+Z) :: "‘ —~’V"‘ 3 (7) )C; ————\W 3 he _% I ha; £”‘&'V#3 3/ /(c M “M” +0 53 \X‘LZV 2- / 7 3 ,l 4th ’ /7— 2‘ + %; ‘nQ. —~2 _' /2 iii. 1- ? y , i“ ‘Z : *‘ DIV xzvi {rams (O‘CML’ ZC3 n Enﬂ‘ 3; ‘)/'L)A __ ._. —' X I 47; : jhlu Lccﬂﬁu 23 L} (.V\ .. C') n 7. True or False (circle T or (14) a) Every monotone bounded sequence converges. b) If E an and 2 bn both converge then Z(anbn) converges. c) If f(:r) : Z bn(ac + 3)” has radius of convergence 2, 71.20 and if lim [bnll/n : B, then B = 2. “HOG d) Let an > 0, bn > 0 for all n and assume that lim a—n : 0. n—>oo bn If 2 an diverges, then 2 bn diverges. 00 e) Let Z an(m — 2)” have radius of convergence 7" = 3. n=0 Then 2 Ian I converges. f) If Zan and 2 bn both converge7 then lim (anbn) exists. ’I’L—’OO g) Iff(a:) 2 :71! :c” then f<">(o) : (my) 4?“ all n. ...
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