math review 1 solutions

math review 1 solutions - x = 1 . 1 and x = 1, we nd: (a)...

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Econ 401 Winter 2008 Math Review 1 Solutions 1. (a) f 0 ( x ) = 4 (b) f 0 ( x ) = 6 x + 1 3 x - 2 3 (c) f 0 ( x ) = 9 x 2 - 2 x + 3 (d) f 0 ( x ) = 7 1+ x (e) f 0 ( x ) = 7 2 x (f) f 0 ( x ) = 3( x 1 2 +4) 2 2 x 1 2 2. (a) (b) 1
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(c) (d) (e) 2
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3. (a) x 1 = 1 4 , x 2 = 239 (b) x 1 = 3 , x 2 = 25 (c) x 1 = 180 , x 2 = 15 (d) x 1 = 20 , x 2 = 40 (e) x 1 = x 2 = 7 4. (a) Since x B 1 = 60 - x A 1 and x B 2 = 120 - x A 2 , substituting into the first equation yields x A 2 x A 1 = 120 - x A 2 60 - x A 1 . Further rearranging yields x A 1 ( x A 2 ) = 1 2 x A 2 . (b) x A 1 = 60 (Note that the axes have been flipped in the figure.) 3
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5. (a) f 0 ( x ) = abx b - 1 (b) f 0 ( x ) = abx a - 1 ( x a + 6) b - 1 (c) f 0 ( x ) = ab x (d) f 0 ( x ) = abe bx 6. (a) ∂f ∂x 1 = 1 (b) ∂f ∂x 1 = 2 x 1 x 3 2 (c) ∂f ∂x 1 = 1 2 x - 1 2 1 (d) ∂f ∂x 1 = a x 1 7. Using the approximation f ( x ) f ( x 0 ) + d dx f ( x 0 ) · ( x - x 0 ) with
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Unformatted text preview: x = 1 . 1 and x = 1, we nd: (a) For f ( x ) = 1 + x 2 , 1 + ( x ) 2 (1 + x 2 ) + 2 x ( x-x ) = 1 + 1 2 + 2(1)( . 1) = 2 . 2 Compare to the actual value f (1 . 1) = 1 + 1 . 1 2 = 2 . 21. 4 (b) For f ( x ) = x , x x + 1 2 x ( x-x ) = 1 + 1 2 1 ( . 1) = 1 . 05 Compare to the actual value f (1 . 1) = 1 . 1 = 1 . 049 . 5...
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math review 1 solutions - x = 1 . 1 and x = 1, we nd: (a)...

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