133-Exam2ASolutions_08

133-Exam2ASolutions_08 - Name Afi$w€r$ Feb 197 2008 Math...

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Unformatted text preview: Name Afi$w€r$ Feb 197 2008 Math 133 — Hourly Exam 2A Do all problems (Total = 100 points). Show all work. Calculators are not allowed. (1) (10 points) Which function grows faster as a: —> oo: 111(m2 + 3:) or In x? Explain your reasoning. ‘ / Q’s-+1 1 I L‘ “a? a T. ‘ (2 +1) . “AM lexwxl : LN va X : LN“ fXUl'xH) x—aoo flu cm x4,” x..,,,o 36+ x W :2, +3“ °° |\ HJxH E lap 92 at; UM ‘, °" =M—=@ x-roo 'ovxs vahaind amé Qanbd 5pm.: or" ‘l‘lae SQ/ML (‘a‘l‘é . (2) (18 points) Differentiate the following two functions. Show all your steps. (a) h(t) = 1n (1 + sinh2(t3)) I _. _‘ A \ 7. ‘_ $s‘nk(‘\?§ ’ C0$M('€’)“ 3*?» k U:\ _ \+ Si‘nl/{L(P) ‘ ‘dl SWAMP” " -\ * s‘\flk‘(&5) ®Y‘ == {L fink San » kn ~ f($)=$3arctancc t e x m x ¥(I*\ : eBQV‘MAW‘EV‘“. c MADAX] Q Nu = fr“ [.2 mt” i 332;in if” N (4) Compute the following integrals (10 points each). Make your method and substitutions clear. 7: IT 1.— . (al/flSinzxdx :- S A04 = S t as ”' @5543 Clay 0 t: o 2' D (b)/tan5xsec3a:dm a: gland“ a. Sgcflx ~ (RCX‘l‘énX thx r ,L L ' 1~~ ~ -« =u—\ duh“- $¢cx~+enx cl}; i) l?“ x — Sec/7k \ 1 3‘ 13‘ :‘%’L\,_2§u"3u *0 2.. ‘3 ,\‘ 3 :él-sec7x'-E$ecx+3€ccx+C (MM,— \ 3 du=7 V“% 3 S x x L = “ggmx- 8—2; x 6" =‘%>{32,m— >341. (5) And to finish: three more integrals (12 points each). Again, make your method clear. dx 1 1' (ED/m “\‘h Sivan '. X "Qx‘ HD " LX'¥\ +j) (b) /ew sinx dx. = lwxezyalc “DZ-\fi utfix‘n X c‘v =€f$2g A“: @5644, v: e: T : $§vxxv 6:]; -- S COS’K A’X MA «3am uzcxss‘x AV=C¥AO V du=‘>$r\x<hc \fsef K = $1M x' 6m —[Qe$’)€~e:x .— SL-smx36 m I: siA‘X‘CJX—‘Cosk'c =9 2.1 = (SM'X‘Los’x\C’X 5° ‘1 = i(smx—coss<\)em kc— “fl”...— X=Q$¢oe éd' c 3 dz: Ix 1‘ _ 9"“ ()Ax2m xfi $-2abfie a \l X'LL‘ 3 9. +29“ 9 X71 XE“ SCIC'BXL ‘ ._ .L 69 " “\ sec, 9 .. i ' e 46- “ ~ L\ 8 CBS 9““ \ O ‘A-Ll + C = L‘ 39“ 9 + C *— E? PL/Uw )‘r‘ X S“ ‘7‘ .1: II A .1: >< Tr .1: If), u —— '? I" A: l OQIO \/ fl ...
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133-Exam2ASolutions_08 - Name Afi$w€r$ Feb 197 2008 Math...

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