Calc Final Solutions - 3 2 3 2 1 lim(3 x 5 x 3 x 11 = 3 2 5...

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1. 3 2 3 2 2 lim(3 5 3 11) 3 2 5 2 3 2 11 21 x x x x - + + = - + + = 2. 2 2 2 2 9 9 9 9 9 10 24 6 4 24 lim lim 13 36 4 9 36 ( 6) 4( 6) ( 6)( 4) lim lim ( 4) 9( 6) ( 4)( 9) 6 lim 9 x x x x x x x x x x x x x x x x x x x x x x x x x x x - + - - + = - + - - + - - - - - = = - - - - - - = - > 9 9 6 lim 9 6 lim 9 x x x x x x - + - = -∞ - - = ∞ - Thus, 2 2 9 10 24 lim 13 36 x x x x x - + - + does not exist. 3. Sent to you 4. R = 20x – 0.01x 2 R = 20 – 0.01(2)x = 20 – 0.02x R (1000) = 20 – 0.02(1000) = 20 – 20 = 0 The marginal profit at x = 1000 is 0. 5. Sent to you 6. 3 4 4 7 3 x C x = + 3 4 3 4 4 2 2 4 3 3 6 2 6 4 2 4 2 6 2 2 4 4 2 4 2 (4 ) (7 3) 4 (7 3) (7 3) 12 (7 3) 4 28 84 36 112 (7 3) (7 3) 28 36 4 (7 9) (7 3) (7 3) x x x x C x x x x x x x x x x x x x x x x + - + ′ = + + - + - = = + + - + - = = - + +
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7. 6 14 70(6 9) f x x = - + 6 13 6 6 13 5 70 14(6 9) (6 9) 980(6 9) (36 1) f x x x x x x x = - + - + = - + - 8. 2 16 0.2 300 P x x = - - 16 0.2(2) 16 0.4 P x x ′ = - = - 0 16 0.4 0 40 P x x ′ = - = = 9. 2 500 6 0.08 C x x = + + The average cost is 2 __ 500 6 0.08 500 ( ) 6 0.08 x x C x x x x + + = = + + 2 2 500 ( 1)500 0.08 0.08 C x x - = - + = - + 2 500 0 0.08 0 C x = ⇒ - + = 2 2 0.08 500 6250 79.06 ( ) x x x x must be positive = = = __ 500 (79.06) 6 0.08(79.06) 18.649 79.06 C = + + = 10.
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