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Math31B_midterm2_Brown_W09

# Math31B_midterm2_Brown_W09 - 1(a For what values of a does...

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Unformatted text preview: 1. (a) For what values of a, does the series 1+ 1 + 1 111a (km)? (1na)3 +... converge? (b) Find the sum of the series 1 1 1 Β§+a+\$+β Note: Part ('0) is not related to part (a). M L E! - 43 β30 β 3 j \ x b 01y (5β ββ-β- β2 (ο¬) 1" L :1 N) 27 heβ Ck)β Aβ, Β£h C\ m β2': β I J < ( (New β5β 1: \ k " I < MM 72 β 1 ,β ox < 1 420 w A u (&>0) ,β nLg . β3. 1 ~95:β f L". [β13)] 1: b d Oi n J ( Γ© ) 2 β6.3-.β β2 ; (E1) :. h;β¬_Β£m V\ :2 { iβ I 1 6 q 1 2. The surface area. of the cone obtained by rotating the line segment 3; 2 an: for 0 g :1: S 1 about the car-axis is \/f_37r. Find the value of a. f ~Β»--β-~ ,. .. L7) : Mβ :[ (X) = 6k [1+ ( {on}; TlWi-Ci" . x 1 WA LC βMk β2 β13-β17 3 CL X L 1 1a a. 0L}? L) -β~ rββββ_/ '9β i m . βrο¬hο¬ {xβ =- 92!β {L\y,β+4;~%ββ( β_- n LLl-βlTC-K?β T M 7?β 3. Determine the limits of the sequences. (@252: 21β52; (5) JLIEIO(1+3nβ1+nβ2)β ,. w ,x .W 31 L .5 p1, mix 3 uΒ») j, k, 1.7.1-2.. , a; 1.-.... 5β1fo nβJJO Q-f-S (Q 11...).00 3+3 1;) , β3' 1 "F . r :11,β Mgο¬a); 1* [1w- - βI: 7 β3β H x -+βU SUCH 1) Q1 X_} 90 5 .1 , .βs ,- _ β )1 LIL Wage, {aw/+3117.β 3 I) '1 K -1 iujrwwwzwr) -1 f a 3 [- J8m+gx + , βw x /Jw~(/+Β§xββ+x )3; "1;. βββ"")(~: X ο¬x β__ 32 β1*;an .7 r.-mw.__._.w__v,_.β~β-'" ,_ :β jm M31 f 3+ 176 ' β4 XβIQP .._. nggο¬ " /" ILV\_ mw-HTMβ "'l 21-1 "Naβ7N IT: + - .. 1 _-pβ 3).. β(W (1+ 3 β1 EH? 1)β : A!Β» U+Β§X βF I) X-βiw 4. Write the Error Bound for 1T1(.97) - f (-97)| where T1(:1:) is the Taylor polynomial for f(:1:) 2: (1 ββ 23:)7/3 at a = 1. (Note: You do not have to ο¬nd 11(3).) 4/ . _ PM) rill-r 3%) 7'31): gig/β21)β? β < - V .βΓ© M) : ~43β ;- (/ wag/4) - (βPMβ) Β«3% If 5MΒ£WΒ’x i Q" ~ ~ Γ© mm x /a β(m/M") I; (X)/ 4-; jigβ"MM? ( [ο¬ 3(1)) /" WWIβ7ββ 5. Use the Comparison Test to determine whether or not the intergral converges. \$._ _' - . f - 3 1 ββ him):- L/DJPOIHβA-J (CL) X337( β40 (:22 6X,'-β9'c Eliβ \$87 βC 00 β2 , 'β I? -2 _ ,_ g 6} 6126 : [(Ilβhx. g ββ :3 ( 7 1:β .. J X / I 2β5 ()0 I 8 517(1 1:00 ( I :(m β~-5~*+-βββ:.L JW 43* we} 11-390 6R 6 E 62.0 f 8 (a Cwβ j ββ I " " βIT β 413-0 Uβ folhvlο¬d) Oο¬Mο¬Γ©/ο¬i 07x10, 43 )(lο¬LnX MM (An/bl e/Lβ *3 Β«β3: '7ββ; XMLβ): 7β r7714 2 β17er S 'Xβlox'x 31"β j 1/} Mtβ A 0 #30 [a 7 βI? r: _/ k! ifβ; ' 5/] JΒ» 1" 00 :: ,(rw X / :,k""f"klβl)+l< ...
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