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Old Midterm (Spring 02)

Old Midterm (Spring 02) - MIDTERM[EXAM CALCULUSJ FOR THE...

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Unformatted text preview: MIDTERM [EXAM] CALCULUSJ FOR THE SOCIAU AND MANAGEMENT SCIENCES Matlfl fi' fipring (There are 6 W E 3111 together they are worth m. You my bhoose t6 do w on E 01 m questionsl m m M M question, as a percentage, is am m [be clean and precise in youn solntionsl I merommend lhatl yom Hisplay all youn working. Do not writd on thd exam paper; Write all M Solutions in thd blue books provided. [1. Thel Eoflowing is thd graph of al fimcfiorfl y 2 W96), fill m delemlind Ehe foflowingj The sign—chart of thd function‘ y 2 fix) Q] The sign—chart of thd deriyatiyd )7 2 Wk] The sign—chart of thd second deriyatiyel E" 2 Wbc] DU not providg w explanation. m FUSE GRAPH] FROM SPRING M MIDTERM [PROBLEM] I bontinued Bl Sketcll thel graphl of any functioil y = tvitll thel following characteristicsj 9 Horizontal asymptotg at y = —2. D m asymptotea atx = l—2 ME 2 Al b x—interceptsl atx: 3122: —3,LZG: 0, andbale p y—intercept at? m : (I b Sign—chart {of Q -|fi|-|-|fi|i|- l—S-3-2 D 4 5 D Stationafi all (—4l4), (2, j, m (7, —3]. i Holes BIA] 2 H andm 2 6i M a large, careful diagramj tld not gravidg w exglanation. 23% —x — x2+2x+ flI-amy: 3_ MWEMZE_4Z. Determine thd following: Q] m m m asymptotea Efy any] (h) )a land M tnterceptq of m (if m Holed of y g (d) Sign—chart bfl M Q] The equation bfl the @ fi y a x : ll. 0] Wgn—cart iii y’ Dd m bfler any explanatiorl [2a]: clearly Show yoan Morkingl Dd m sketch ma graghl 93% Al mmmflgraphiadrawmimmmm H onthepreviouflgggiflthdderivativd M = L’- ofl a functiorfl y 2 lwithl Which [I] am working. (Notel Ifl isl thel graph ofl the derivatin M = f’ (x) non of thd functiorl y = M.) (a) [Find landl analyze the vertical asymptoteg of the functiorl y = fig) E] Find and analyze the htationarfl points ofl thel function 34 = f (x1 (0] Determind whetherl the graphl oil y = fig] id concave up or concave tlowrl an the pointsx= find: ix: —fl,,andx=4. Maw small diagrams ta depiczl ma type ofeacll LA bad SP, bad Lgivel brief reasons for all W amwem 20% Eontlnueil] 51 mmemnealeahldisitghemnfmnjpowerplantaflapointW QnQnehankbflariventhafi is 201] ttneters widd to a [actorx at point B on the ppposite bank bfl the river m ttneters denstream from Al The cabld fl run id a straight line from A! alfig the bank\ for a certairidistancetgamamthe—Mkasflandtheninaistraightfinefife @1113; Edmbflthdmflnflthdbahldthatm‘[email protected];flfimsttl theflpart thhe eahlel thatnms undefihvateris $13 permeteL LEXpress thd Intafl best thhe cable as a functiorfl ofl thd distance from A to Q Clearlg denote Mat eaclfl of your Mics grands [on 117% E His agenera! facthCZlcnlns that, fiffliederixatixe Qflthdhmctinnyzflx] i3 M = .p them the derivativd Qf thd funetiQn W—x is —g(—x . KSOJ thr instance, sinee @:6)d— 9M = 69d 51 it tfollows thafl (at xfl 3( x) —9)' = —(6( x) 5).) Givd a —fige0metrzc explanation bfl this general tfactJ Clear] disglax all thd stegs of youfl 117% Pk>X<>X<>X<>X<*******>14***********$$$*****$$$$>fl ...
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