Exam 1 - Ch 2 - Fall 2004 - 2 = x , but not differentiable...

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Survey of Calculus Exam #1 Thursday, September 16, 2004 Name ______________________________ You must show all your work on this paper. Solutions without correct supporting work will not be accepted. 1. Use the graph given to evaluate the limits: (3 points each) a. ________ ) ( lim 2 = + x f x b. ________ ) ( lim 2 = - x f x 2. Evaluate the limits without using a graphing calculator or making tables. (8 points each) a. ( 29 [ ] 2 / 1 25 5 lim - + t t x = __________ b. 15 8 3 lim 2 3 + + + - x x x x = __________ 3. Given 8 2 3 ) ( 2 + - = x x x f , find ) ( x f using the definition of the derivative. (10 points) 4. Given 2 2 ) ( 2 - + = x x x f , find: (5 points each) a. the average rate of change between 2 = x and 5 = x . b. the instantaneous rate of change at 2 = x .
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5. Find the derivative. Do not simplify your answers. Circle your answers. (7 points each) a. 5 3 4 5 5 3 ) ( x x x x f + - = b. 5 1 3 ) ( 2 2 4 + - + = x x x x g c. 3 5 2 2 ) ( - = x x x f 6. Draw the graph of a function that satisfies the conditions given (if possible): (5 points each) a. The function is continuous at
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Unformatted text preview: 2 = x , but not differentiable at 2 = x . b. The function is defined at 1 = x , but ) ( lim 1 x f x does not exist. 7. Given 3 27 x y = , find 8 2 2 = x dx y d . (7 points) 8. If the cost of purifying a gallon of water to a purity of x percent is x x C-= 100 100 ) ( cents for 100 50 < x , a. Find the instantaneous rate of change of the cost with respect to purity. (5 points) b. Evaluate this rate of change for a purity of 95% and interpret your answer. (5 points) 10. A companys profit function is 200 6 ) (-= x x P dollars, where x is the number of units. a. Find the average profit function. (3 points) b. Find the marginal average profit function. (4 points) c. Evaluate the marginal average profit function x = 10 and interpret your answer. (3 points)...
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Exam 1 - Ch 2 - Fall 2004 - 2 = x , but not differentiable...

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