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8 Pages

### S1Prof_05_05

Course: ECONOMICS 102G, Spring 2011
School: Uni. Iceland
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Word Count: 887

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Akureyri Viskiptadeild Hagnt Hsklinn strfri I Endurprf jn 2005 Dmi 1. (10%) Markai er lst me eftirfarandi jfnum: Frambosfalli P = 1 QS + 20 2 Eftirspurnarfalli QD = 296 4 P ar sem Q er magn og P er ver. a) Teikni ferlana upp hnitakerfi og reikni t jafnvgispunktinn b) Finni hagsbt seljandans (PS)(framleiendabata) jafnvgispunktinum c) Ef lagur er 25 % skattur hverja einingu, finni jafnvgispunktinn og...

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Akureyri Viskiptadeild Hagnt Hsklinn strfri I Endurprf jn 2005 Dmi 1. (10%) Markai er lst me eftirfarandi jfnum: Frambosfalli P = 1 QS + 20 2 Eftirspurnarfalli QD = 296 4 P ar sem Q er magn og P er ver. a) Teikni ferlana upp hnitakerfi og reikni t jafnvgispunktinn b) Finni hagsbt seljandans (PS)(framleiendabata) jafnvgispunktinum c) Ef lagur er 25 % skattur hverja einingu, finni jafnvgispunktinn og hagsbt seljandans (CS)(neytandabata) d) Finni tekjufalli TR , jaartekjurnar MR og a magn Q sem hmarkar tekjurnar Kennitala: Sa 1 af 8 Hsklinn Akureyri Viskiptadeild Hagnt strfri I Endurprf jn 2005 Dmi 2. (10%) Finni gildi x til a jfnurnar standist. a) log x x = ex x 5e x b) 10e 0.5 t dt = 15 0 Kennitala: Sa 2 af 8 Hsklinn Akureyri Viskiptadeild Hagnt strfri I Endurprf jn 2005 Dmi 3. (15%) a) semur um a greia 12.000.000 kr. skuld 25 rum me jfnum greislum mnaarlega, fyrstu greislu eftir mnu. Hve miki ttu a greia mnui ef rsvextirnir eru 4,2% og reiknast mnaarlega. b) tt 587,39 dag. Eftir hve mrg r ttu 1000 ef boi eru 9% vextir sem eru reiknair risvar sinnum ri.. c) tt 10 000 kr. dag. Hva urfa vextirnir a vera ef villt eiga 50 000 kr. eftir 15 r. Vextirnir eru reiknair risvar sinnum ri. Kennitala: Sa 3 af 8 Hsklinn Akureyri Viskiptadeild Hagnt strfri I Endurprf jn 2005 Dmi 4. (15%) 5 x3 a) Diffri falli f ( x) = b) Diffri og finni jfnu snertilsins, egar x = 1 f ( x) = ln c) 4 2 x2 og einfaldi tkomuna ex +2 x3 Finni diffur, egar (x,y) = (1,1) og (dx,dy) = (0.1,0.2) z = x2 + y (3 x2 ) 3 og finni einnig jfnu snertiflatar sama punkti Kennitala: Sa 4 af 8 Hsklinn Akureyri Viskiptadeild Hagnt strfri I Endurprf jn 2005 Dmi 5. (15%) Noti afer Lagrange til a finna bestu lausn fallsins (max/min) f ( x, y ) = 160 x 4 x 2 2 xy 6 y 2 + 200 y annig a x + y = 36 Kennitala: Sa 5 af 8 Hsklinn Akureyri Viskiptadeild Hagnt strfri I Endurprf jn 2005 Dmi 6. (10%) 1 1 A12 10 Gefi er A fylki = 2 12 1 og hjttafylki A. cof(A) = 110 1 10 1 6 6 A33 8 a) 2 Finni A12 og A33. 8 2 1 b) Finni kveu og margfldunnarandhverfu fylkisins A = 2 12 1 . (detA og A-1) 110 c) Finni gildi x og y svo jafnan standist x2 5y 2 15 = 5 20 SKILI SVARINU ME ALMENNUM BROTUM OG SNI TREIKNINGA! (annars fi i ekkert fyrir svari) Kennitala: Sa 6 af 8 Hsklinn Akureyri Viskiptadeild Hagnt strfri I Endurprf jn 2005 Dmi 7. (10%) Smiur sem lti trsmaverksti br til bor (x) og stla (y) sem hann selur til virulegrar hsgagnaverslunar. Hsgagnaverslunin getur selt alla framleislu smisins. Smiurinn selur hvert bor me 30.000 kr. hagnai og hvern stl me 10.000 kr. hagnai. Af heilsufarsstum getur smiurinn ekki unni meira en 40 klukkutma viku. a tekur smiinn 6 klukkutma a ba til eitt bor og 3 klukkutma a ba til einn stl. Hsgagnaversluninn fer fram a fyrir hvert bor sem a kaupir fylgi minnst rr stlar. Hsgagnaversluninn ltur skja borin og stlana til smisins einu sinni viku, a gerir a a verkum a smiurinn er vandrum me geymsluplss. Hvert bor tekur jafn miki plss og fjrir stlar. Ef bara vru settir stlar inn geymslu smisins vri hgt a setja 16. stla anga inn. Hvernig smiurinn a skipuleggja sna framleislu hverri viku annig a hann hmarki sinn hagna? a) Riti hagnainn sem fall af x og y. b) Riti skilyrin sem fall af x og y. c) Teikni jfnurnar inn hnitakerfi og aukenni lausnarsvi vandamlsins. d) Hver er hmarkshagnaurinn? e) Hver arf hagnaurinn af hverjum stl a vera svo smiurinn bi bara til stla. Kennitala: Sa 7 af 8 Hsklinn Akureyri Viskiptadeild Hagnt strfri I Endurprf jn 2005 Dmi 8. (15%) a) Leysi eftirfarandi mismunajfn og lsi eli lausna (teikni) y t = 0,8 yt 1 + 18 b) y0 = 25 og finni yt egar t stefnir ndanlegt. Markai er lst me eftirfarandi fllum QD = 500 P QS = 1 P + 200 2 dP = 0.4 ( QD QS ) dt P(0) = 250 Finni formlur fyrir P(t), QS(t) og QD(t) og kanni niurstuna egar t stefnir endanlegt. Kennitala: Sa 8 af 8
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