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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 §+a+$+” Note: Part ('0) is not related to part (a). M L E! - 43 ‘30 ’ 3 j \ x b 01y (5‘ ——-—- ‘2 (fl) 1" L :1 N) 27 he“ Ck)“ A”, £h C\ m ’2': — I J < ( (New ‘5‘ 1: \ k " I < MM 72 ‘ 1 ,“ ox < 1 420 w A u (&>0) ,— nLg . ’3. 1 ~95:— f L". [’13)] 1: b d Oi n J ( é ) 2 “6.3-.“ ‘2 ; (E1) :. h;€_£m V\ :2 { i“ 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 ~»--—-~ ,. .. L7) : M“ :[ (X) = 6k [1+ ( {on}; TlWi-Ci" . x 1 WA LC “Mk ‘2 ‘13-’17 3 CL X L 1 1a a. 0L}? L) -—~ r————_/ '9‘ i m . ‘rfihfl {x— =- 92!” {L\y,—+4;~%——( —_- n LLl-‘lTC-K?‘ T M 7?’ 3. Determine the limits of the sequences. (@252: 21—52; (5) JLIEIO(1+3n‘1+n‘2)” ,. w ,x .W 31 L .5 p1, mix 3 u») j, k, 1.7.1-2.. , a; 1.-.... 5’1fo n—JJO Q-f-S (Q 11...).00 3+3 1;) , ’3' 1 "F . r :11,“ Mgfia); 1* [1w- - “I: 7 ‘3‘ H x -+‘U SUCH 1) Q1 X_} 90 5 .1 , .‘s ,- _ — )1 LIL Wage, {aw/+3117.” 3 I) '1 K -1 iujrwwwzwr) -1 f a 3 [- J8m+gx + , ’w x /Jw~(/+§x”’+x )3; "1;. “‘“"")(~: X fix ‘__ 32 ”1*;an .7 r.-mw.__._.w__v,_.—~—-'" ,_ :— jm M31 f 3+ 176 ' ’4 X‘IQP .._. nggfi " /" ILV\_ mw-HTM’ "'l 21-1 "Na—7N IT: + - .. 1 _-p‘ 3).. ”(W (1+ 3 ’1 EH? 1)” : A!» U+§X “F I) X-‘iw 4. Write the Error Bound for 1T1(.97) - f (-97)| where T1(:1:) is the Taylor polynomial for f(:1:) 2: (1 —— 23:)7/3 at a = 1. (Note: You do not have to find 11(3).) 4/ . _ PM) rill-r 3%) 7'31): gig/’21)”? ” < - V .‘é M) : ~43— ;- (/ wag/4) - (”PM”) «3% If 5M£W¢x i Q" ~ ~ é mm x /a ”(m/M") I; (X)/ 4-; jig—"MM? ( [fl 3(1)) /" WWI—7““ 5. Use the Comparison Test to determine whether or not the intergral converges. $._ _' - . f - 3 1 ‘— him):- L/DJPOIH‘A-J (CL) X337( ’40 (:22 6X,'-‘9'c Eli“ $87 ‘C 00 ”2 , '— I? -2 _ ,_ g 6} 6126 : [(Il’hx. g “‘ :3 ( 7 1:“ .. J X / I 2—5 ()0 I 8 517(1 1:00 ( I :(m —~-5~*+-—’—:.L JW 43* we} 11-390 6R 6 E 62.0 f 8 (a Cw“ j ‘— I " " ”IT ‘ 413-0 U“ folhvlfld) OflMfié/fii 07x10, 43 )(lflLnX MM (An/bl e/L‘ *3 «’3: '7‘“; XML“): 7‘ r7714 2 ‘17er S 'X’lox'x 31"“ j 1/} Mt“ A 0 #30 [a 7 ”I? r: _/ k! if”; ' 5/] J» 1" 00 :: ,(rw X / :,k""f"kl‘l)+l< ...
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