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Sample Midterm 3 solutions

# Sample Midterm 3 solutions - Name and SSN M 408C Exam 3...

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Unformatted text preview: Name and SSN: M 408C Exam 3 Reid Fall 2001 71/2 _ 1. Compute the deﬁnite integral / eS‘mcos xdm. (15 points) 0 L64 U:Sun5( ,Tken CL): COSKAX H x:o, uzsmzmjo \1Cx:"‘/2I ch‘n(ﬁlz\:\, m m WW Laws k x U ~‘ \ \$0630: {NO- e-eb=e,'~\.—e,—\ 2. Compute the indeﬁnite integral / 2:4lna: due. (15 points) —T’\’\\S \5 om “/1“?ng 01D H/‘e ﬁofm IUJV’ Wkere u: Ynx‘ Av: XL} ix S = 5‘ - | J L‘J X my -—-— . S 5‘ X K _ S : X5\WX '- L T C 5 25 = :i (w ~15) "‘ C we. cam/\(‘ZM‘LC 3. Decide whether the following functions are one—to—one on the domains indicated. You must prove your assertions to get full credit. a)f(:c)= (x2+1)e“ on(— 00,00). (8 points) E ii: i) J Cir )\,\¢._ {1 :(Zx‘vo‘ixhax 4’3‘(é—X(KZ+\\)\ :ZCx “\e‘) +3 (2X) = e‘(>«2+\+2>0 =€f (xz+2x+\) :CK(X+‘)Z7O ‘ch a“ ma\ X This fig shawls \Wcremsxn3,so A is ﬁne—ArOPO-ﬁe (b) f(:c)= sin(xT+1), :1: #0. (7 points) H: K: i sm(><+|): sm(Z‘) we um“ “‘Y’mj omeUner f0 ai‘ ﬂit} Such *L‘C’V" S\V\(gil_) :S\V\( (2‘) | Provinj Hm} f ‘3 Mai Ome- +0 OWE, g FWSXV W01Le H404 m 3v€te(‘0\\ SM [9\—.3m( (9*ZTI‘)‘, \”\€’\C€ \4 iﬂ-PZTY: Z cog, Lou/63 Shﬂ/ﬂ) - SVALZ» as AeS:rel_ (j 'H S O\v\mj ‘por (j m krin¢ CXPresSion 3? +27TZZ/ WQ DUNN] 9:8; : 2—211 (j—k’: ('2 ZTF)3 i: (2 211%, 3 1:3(I2Tr> ——"""" Ti is ie. €5,re CM. 35%”, iii HA if} 4.(a) Sketch the region Q bounded by the curves y = x2 + 1 and y = 3 — 2:2. (5 points) (b) Find the volume of the solid of revolution obtained by rotating 9 about the x—axis. (15 points) 3.1? Tkle, féc4dw3\e aLove \s ﬂwen L 1 A‘g‘kgy r0 qulomi :11 3° E‘ xZ-ﬂ 'H/U3 LECOWS a WASLer; [zxjﬂ Thain“), He Vo‘ume is jwmhj \}:§1V[(3-3ﬂ_(x+ﬂ]dx ‘57 SMWJW‘IV ‘OZJ “R3 ’ﬂ “ZR HHJK = 2n 5( 0[(<1— (054 m“) (K (a “WK ‘ 2ﬁfo( (854 +83% :uﬂj (wxnx :\tw[l‘g— H]; :ié71(3\/3 +l) :- 3;? 3 4 5. Find anti—derivatives for the following functions: (a) %. (10 points) 032 weal A’o ‘anj 5\$W‘(ZX) 4X 5*COSCZX) Lax u : 3+L03V2ﬂ ‘-T\r\en (Jo: -23w\(2x)i>( . TLe—m‘core, SM 1 «l- 2.\$\V\(Z)(»J)( _ ZJA—U 3+cosL2x) 7‘ 3+ (05 (2x) (1 \ ‘21nu+C ”2'. \n (3‘+(_os('2x)) 1" C 6. On which intervals is the function f( :17): we“ increasing/decreasing?( (15 points) Prsf1éwe COMPAQ {(Q .osmg C\"Aw\ m\e cmg “mg “(MA at _ PLOVA¢r1VoA~xve\$ o 1M: XQ: (41) +6 ?onen-\ex14\s ’ Theregora 7cm.) \3 \ncreas‘hﬂ 0" ( (M003. JCCY‘CQSHACJ on ...
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Sample Midterm 3 solutions - Name and SSN M 408C Exam 3...

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