StA_verkefni_11_lausnir[1] - Hskli slands Viskipta og...

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Háskóli Íslands Viðskiptaskor haustið 2009 Viðskipta- og hagfræðideild Stærðfræði A fyrir viðskiptafræðinga. Heimadæmi 11 Lausnir 1. Finnið óákveðin integröl eða stofnföll fyrir eftirfarandi föll: a) ( 29 2 10 10 2 3 0 0 40 2 20 10 2 40 2 20 20 42,16 3 p q q CS q dq q q = - = = = - - = - = b) 5 ( ) 2 f x x x - = + c) 2 3 1 ( ) f x x x - - = - Lausnir a) 6 3 ( ) 5 6 3 x x F x = + b) 2 4 2 ( ) 2 4 x x F x - = + - c) 1 3 ( ) ln 3 F x x x = - 2.. Reiknið eftifarandi ákveðin integröl: a) ( 29 3 3 2 2 4 3 x x dx - + b) ( 29 3 0 2 x x e dx + c) + 6 2 3 2 3 dx x x x Lausnir a) ( 29 3 3 4 3 3 2 2 2 73 4 3 4 3 4 3 12 x x x x dx x - + = - + = - b) ( 29 3 3 2 3 0 0 2 8 28,09 x x x e dx x e e + = + = + = c) 6 2 6 1 3 2 2 x 3x dx x 3ln x 3,63 x - + = - + = 3. Finnið neytendaábata miðað við gefið jafnvægisverð : 20 * = p a) 100 p q = - b) 1 25 p q - = c) 2 40 2 p q = - Lausnir: a) ( 29 ( 29 80 80 2 0 0 100 20 80 100 20 80 100 20 80 3200 2 2 p q q q CS q dq q = - = = - = - - = - = = Kennari: Guðmundur Ólafsson lektor Síða 1
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Háskóli Íslands Viðskiptaskor haustið 2009 Viðskipta- og hagfræðideild Stærðfræði A fyrir viðskiptafræðinga. b) ( 29 [ ] 1 1,25 1,25 1 0 0 25 25 20 1,25 20 25 20 25ln 20 p q q CS q dq q q - - = = = = = - = - = ∞ c) ( 29 2 10 10 2 3 0 0 40 2 20 10 2 40 2 20 20 42,16 3 p q q CS q dq q q = - = = = - - = - = 4. Finnið kostnaðarföll ) ( q C C = og tekjuföll ) ( q R R = , þegar eftirfarandi er gefið: a) 150 2 MC q = + Fastur kostnaður 200 F = 2 150 2 150 200 MC q TC q q = +
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