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# exam-final - MAC 2233 Final Exam Spring 2007(4 points...

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Unformatted text preview: MAC 2233 - Final Exam Spring 2007 (4 points) Evaluate the following limits: (a) lim (52!:2 +3203 +2x+x5) m—>—oo hm (gxq’Jr3x2’L1xLxsl 2: Xa—m in“, (KS). 4,, X4 \$3 J32: +1 b l —-——-————-———- ()ziIPoo5x-l-2m4-l-3zc2-l-a: th ¥\$*3X541 , ' '3XS X‘lbo" gx+fxtlfgx2+x X~a-ao ﬂxq 0m. Li. .. “wish “h" MAC 2233 Final Exam Spring 2007 (4 points) Evaluate the following limits: xaH’ =3? Qim 2X“ 2: *Oo xaq’ X»H (b) 11m 73,2 ‘*an -m¥:1.w , “‘ £ “’3' (xezYi m2“ x4 MAC 2233 A Final Exam ' Spring 2007 (4 points) Consider the function ' f(a:) = m4 — 2x2 (1) (a) Evaluate and factor the derivative f’(.7:). l‘LxMx’~5l-2x: Hthx = Hxina) ~. LLX‘CXJGLQ’ (1)) Evaluate and factor the derivative f”(.1:). We LHx3 un’ lix H HL3x 0 LL“, X»[)CFM+1) U MAC 2233 Final Exam ' Spring 2007 (6 points) Continuing the previous question: ‘ (3) Use a, table of signs to determine the monotonicity of f(x) Zevocs: 0,4:1 / \ f {lfﬂmﬂ (b) Use a table of signs to dete1n1ine thec convexity of f(x) (o) Create a combined table of signs for f, f’, and f” to Show: combined monotonic- ity/convexity, min/max points, and inﬂection points. MAC 2233 ' Final Exam ' Spring 2007 (4 points) Consider the function f(:v) z (51:2 m 456 + 5)e\$ ‘ (2) (a) Evaluate and factor the derivative f’ (4r) PM 7:— [CxMx Wife-"(Jr 0(th} 9) (6%)] (ix—L139" + [Xi‘auskx ins—m 9 +2300 6" , :‘(X2-23<+ 0e“ . ‘= (X-tﬂex (b) Evaluate and factor the derivative f” (.73) MAC 2233 Final Exam V Spring 2007 (4 points) Continuing the previous question: (a) Use a table of signs to determine the monotonicity of f(X) 5? j 0} (mm) eml (4,“) Ll am no (1mm M Ma Q”- pthiMuow 01L X=i. (b) Use a table of Signs to determine the convexity of {(X) 1 am“ up 54 (”00(4) «mi (”+0.2 {convex atom A (~11!) MAC 2233 ‘ Final Exam Spring 2007 (4 points) Evaluate the integrals and simplify your answer as much as possible 1x12 (a) / ezdx 0 0 z 2 l X 3x 1: {17+ 2 lixo - l 3 - ﬁ+3\$+fré ~ —-—-—+————~ 1 «V .2 %~ 1 l G l. 1+5 19. 23 A .—ns_- WA ...
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