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Mock Exam 4_solutions

# Mock Exam 4_solutions - Mock Exam 4 KC 5%— Mthsc 108-05...

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Unformatted text preview: Mock Exam 4 KC 5%— Mthsc 108-05 Fall '07 1. What Is the 3rd order Taylor polynomial for f(x)= ix :1 = 3? a. P3(x) =E+Z(x_3)+1(x_3)2 +§(x—3)3 .500 = —§+§(x—3)—§(x—3)2 +irx—3)3 1 c. P306) = —§+i(x—3)—:—(x—3)2+§(x—3)3 d. P305) =§—41(x—3) +%(x—3)2 —%(x—3)3 2. What if a=0 for problem 1? ,P3(x)=1+x+x2+x3 ‘5, P300=1—x-l-xZ—x3 c. P3(x)=1+x+2x2+6x3 —__l l _l 2 i 3 d.P3(x)— 2+4x 8x +169: 3. ”2:21 an = 1, then limwmO an = a. 4 @ c. 1 d. 2 n3 n x 4. Find the radius of convergence of the series 235:1 311m a. R—O W [MD M\ b.R=l I900 3 Wk W7“ c. R=1/3 (d.R=3) ilk/m Hg} Ll e. R=°° “#00 129. Al 3 m“) 5. Which of these diverges? a as = e b {an}=[(—1)“§] @2321; Wwﬂ d 255:1 4)“; 6. Find a formula for the general term am for n31, of the following sequence: {1,—3, 1,—ﬂ, ...} “‘1 7 49 343 n —.-.\ «:7 \ 't‘ _i - 9a a' ( 7) “2} _‘:'_"..7 “‘ -__. .._. b (—1)(3)"_1 — —- Li]. I 7 1 n ._._ H— 4C.“ Ji— n— 3 TL— .. QM) 1(21 n =Ar = 21% _ d (—1)“ G) i“: n—1 WW 3; h” e (—1)"(§) H) K1 . . 1 1 1 1 _ 7. The sum of the geometric series 2 — 1 + E — — + — — — + I5 33' P- . {D 0 WIN 4: I-| elmwle Ma ﬁg ’1“ SW “é. u g.) ll ﬁzlwh‘d 8. Convert the following to Cartesian: rsinB = lnr + IncosEl 2 y=ln( x +3!2 + ,x—x2+y2) Oy=1n(x) c. x: 1110/) — 2 d.x—1n(x +y2 +W) 9. Convert the following to polar: x2 + xy +y2 = 1 1 . i” = —- a 1+3in96036 2 1 T = ,— ' . 1+5m6'c056 c. r2 + rsinﬂcosﬂ = 1 d. r2 — rsinﬂcosﬂ = 1 10.Construct the following series: 1‘30): 0 M1 Q a Taylor series for the function f(x)- — lnx a- — 1 . __._ .1. no - Ion-> 0‘40”” alk‘fx‘lll-l- ? kX- \33 -' At“ 04 “0.- x CD “Uh-I ”‘0“ ‘P U)" -l E’- Z l - WU) '= 2 2: hi. h 7‘5. W) ="Lc “i;- b. Series for the function f(x) = xsin(3x)? /‘ SMX': X .E f B: 35:! 3‘ 5‘ 1i .. 5V0 3x: ax — (as? f Bi L333] 113+ first 4 3""? A 5‘? 7‘ terms. st-n'ax-- 3x2 mix BAP’ BMBXP ﬂsxﬂ . c. Series for the function f(x)— _ 6‘5 ? 5‘ '1". erl “FINA? I—Ik‘3 2i €u\—1X‘I"L,—1T iii gr .2 _\__ 23k . (-10; -2)?I?’.+_ was \K‘ha X8 "ii—Tr; gilx'fi 11.Te|l if the following sequences converge or diverge. If the sequence converges, give the value and explain your reasoning. a. {1, v’Z W. W, ...} Ell-h} 2 “All“ mm W :— Moo 4‘” \ {W'VWS b. {1/3,2/3,1,4/3,5/3,...} gang: {3;- m-aoo 5 d l Vamp 12.Te|| if the following series converge or diverge. If the series converges, give the value and explain your reasoning. oo 5 ' ' I 3 '36 a. 27.212.-. Wtwo EKJHLS 3 ii WI 00 511 -- CD 6“ -* a: 5- f: QS b 2.-.? ’Z “in" Z. a" i’ Q“ m “'4 l- . aw fl c. 2m (:1)! {adorns}. 2-? (Q‘Filcm‘tH than)» m rm Km“?- “ﬁrm (hi-I‘l)‘ m—kh “500 W. " h ; m n+\ ( 1.)) J W m i” M .__L_ _ “-200 hkryﬂ. n mam n1 3%. YWOD 2Y1 14.What type of symmetry does 1' = cos (9/2.) have? Graph the function then ﬁnd the area bounded by it. ...
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