Final MTH251 Fall10 PRACTICE with KEY

Final MTH251 Fall10 PRACTICE with KEY - Practice Problems...

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Practice Problems for Final Exam MTH251 KEY is at the end. Note: This is good practice, but it is NOT a comprehensive list of material covered. 1. A parking lot charges $3 for the first hour (or part of an hour) and $2 for each succeeding hour (or part), up to a daily maximum of $10. a. Sketch a graph of the cost of parking at this lot as a function of the time parked there. b. Name all the values for which this function is discontinuous. 2. 2 lim 2 - - + x x x 3. a. What specific property does ) cos( u possess that allows us to say ( 29 ( 29 x x x x e e - - = lim cos cos lim ? b. Determine the value of this limit if it exists. 4. ( 29( 29 1 2 2 5 4 lim 2 2 4 - - + u u u u . 5. x x x + + - 4 1 4 1 lim 4 6. 12 3 lim 2 2 3 - + - x x x x x 7. Find the derivative of 1 2 - + = x x y 8. Find the derivative of ( 29 r e r r y 2 2 - = 9. Find the derivative of ( 29 2 2 cos 1 sin ) ( x x x h - + = .
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10. Find the derivative of ( 29 x x x f 2 ln ) ( 2 + = . 11. Given 6 2 2 3 = + + + y y x x , find dx dy using implicit differentiation. Note: you may leave y -terms in your final answer. 12. Find the equation of the tangent line to the curve x x y 2 2 - = at the point ( 2, 1 ). 13. Use derivatives of f to find the local maximum and minimum values of 5 6 ) ( 2 2 1 3 3 1 + - - = x x x x f . Be sure to indicate which values of x produce the maximums and which produce the minimums. 14. A stone thrown into a pond produces a circular ripple, which expands from the point of impact. When the radius is 8 ft., it is observed that the radius is increasing at the rate of 1.5 ft/sec. How fast is the area enclosed by the ripple increasing at that instant? 15.
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Final MTH251 Fall10 PRACTICE with KEY - Practice Problems...

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