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Final Exam- Vancouver 2008 - Math 202-02 Final Exam Spring...

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Math 202-02 Final Exam Spring 2008 Name: ID: Date: Directions: Please show all work unless specified otherwise. You may use a basic scientific calculator, but no graphing calculators. Use proper notation. 1. (12 pts) Evaluate the following limits. Show all of your work or justify your answers! (a) lim t →- 1 t 2 + 3 t + 2 t 2 - t - 2 x 2 10 1 6 4 2 8 0 y (b) lim x 1 f ( x ) where f ( x ) = ( x 2 + 4 x if x < 1 , 3 x 3 - x - 1 if x 1 . (c) lim x →∞ x 2 + 2 x 2 x 3 - 2 x + 1 2. (10 pts) Use the limit definition of derivative to show the derivative of f ( x ) = 6 x 2 - 4 x is f 0 ( x ) = 12 x - 4. No credit will be given if the limit definition of derivative is not used.
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3. (30 pts) Using the derivative rules developed in class, find the derivatives of the following. Do not simplify your answers. (a) r = 1 3 s 2 - 5 2 s + 7 s 2 + 1 - ln s (b) g ( x ) = (2 x 3 - 4 x + 7)(4 - x 2 ) (c) v = 1 + x - 4 x x (d) y = 17 t - 3 8 t - 1 (e) y = 3 e 4 x + x 2 (f) y = ln x ( x 2 + 1) 5 1 + x 2
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4. (8 pts) If the profit function for a product is P ( x ) = 20 x + 1, find the marginal profit when x = 15 and interpret the result.
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