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Math31B_Brown_Final_W09

# Math31B_Brown_Final_W09 - 1 Determine whether the series is...

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Unformatted text preview: 1. Determine whether the series is convergent or divergent. [/OfM «1,160 :0: x/n—5:—_2n2 (b) :molggn L10 MMVE I ( Vi CL) (“v A M : VI; “/9 ): 2/ We :4 1"“ t-ﬂ’x "‘ 11"" ['3/3 m-aoo ””3 H600 High “—900 n W5 00 A0 WWOOWL £5 1 06 00) ‘02— If : if 2/99“}; Lit/L4, % m 31h kg; ha 14"; 5 (37C .1— u-(J’u 2 L a —/€/wL/€Jh X] m 710% W x J» for 2. Evaluate the integrals. [[0 [Jo/wk} (a) f x _I dx (1)) fcos(ln\$)d:c [/0 Wong-LI] (O‘JM 3A— +B7C‘_+C _A)(2+ +3y1+CX +ﬂXTIC U’HNXQ‘W) X+r 7(14. [ (Hum +0 A'f‘gﬂl KfC:‘l/)¢+C- O A:’%: OCT?! 3 I “f C w u, ”MM 3. Find the interval of convergence of the power series (—5)” h'ﬂ]; Mi?! ha“ 11:2: owﬁ #9..» £(LL) 2,5 M 3 V1990 2‘ ”‘4' 3k 2 CmW/au “tr” X‘{[( /5 70 2 00 V1 2 K :t/Y‘L _. , “"P' - .2 n / W (-2—) 4. Calculate the limits. Ue‘ooa J1] (a) 5135 Sin—E” (b) 3330 (wily f,- u Pox-ark] "“ xx #1 , L(”U/Em M 7: T; rim W I X‘ﬁo X I/ 7540 52/1 “54? all» (I HX‘3‘“ .2\__[ “ii“ 4:31": {1 #X2) (“(2%) “' . “'7' lrm 26-9 0 39(13/ H X-ﬁo éX :ﬂlh‘ W :- J" Xﬂo ‘49 6 x A X L19) : (ABET) jw L j *‘Jm 1/2““(2'17 5L X+ Kw)” ( X24900 1 I J! nX’j/VIOC‘H) 132“” X ﬂX‘H a 95.4w 7”! H 36-400 ‘Xﬂl (ia— A “1 {W ”M t/QNA— _. cg/ﬁ —’ “I yaw “' 783‘ >64 00 X +X 6 f [D Joni 01' 1L4? :1 5. Let f(:1:)= ln( (.3—1—22) (.21) Find he Maclaurin polynomial T4(x) for f (x) (b) Find the radius of convergence R for the Maclaurin series T(:L’) for f( (at) l: I 0 Po/tﬁﬁ'] ((M7f1x‘1“ﬁw[§f?0 {/0}: £2“? 11%) — 3%;me 70201: 4' Wm :e um”: ' 50) if iii/(2c) “Jew-11)”? {5/ P H LP“ 1: «(5. PM) '5' ~W5) (31qu j“ A”) AP] V j ‘/ 02 ’3 5 (K)’/€«n§+ﬂ/:X‘§%y2+%gi7 -971fo TM) in 3 + ZCOW (h’n ”fa—"X 7 6. Find the maxima of the foilowing functions on [1, 00). (You do not have to use a _ derivative test to Show that it is the maximum.) (iDmeqtd (a) f(:c):l—:§gi (b) f(\$):\$e—a:2/8 [[0 Wings] "f ,3 ‘ a R vallm'r—Xxﬂdzmx :,_3:lm2:0 X X V3 3ihX:( L71“ V? X38 7. Determine whether the series converges absolutely, conditionally or not at all. {tofoznﬁ‘k (a) f: COS” (a): (1)” [/D fm’h‘ﬁj ”=1 coshn n=zA/— nlnn QM /%/ 2 M (.11 ﬂ cit/{450 w WWCJ L “IQ;- Lai :fmﬂ W a AL new] WW 8. Given that 26%? (@g fie: : ‘2 (1.. )1:2_o¥ Era—0L 10 9. Determine Whether thejmproper integral converges or diverges. Do not attempt to evaluate the integrals. (a) f: 1n(5:/-_3:-1) dm _ (b) [100 35%;? v 3/: l ,L (jib Wecﬂﬂv m%>)c ll 10. Calculate the area of the region of the plane bounded by the curves 3/ = are\$2 and y = 33/6“. ( 2 1 a 76 — 9c _ 9C - ' MK "95‘“ ’L 9’“) 5T 6 '6 .I/r/W‘FII AIR—Jr guxmi (QHK #01 X 6X2 2.?(6'7‘ [LUVLJJ-cmeq 1L6K' :61) ’46 ...
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Math31B_Brown_Final_W09 - 1 Determine whether the series is...

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