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224pracfinal

# 224pracfinal - MA 22400 Final Exam Practice Problems The...

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MA 22400 Final Exam Practice Problems The Formula Page (available on the course web site) will be attached to the final exam. 1. Evaluate Z 2 x - x dx. A. ln | x | - 2 x + C B. - 2 x 2 - 1 2 x 1 / 2 + C C. 2 ln | x | - 2 x 3 / 2 3 + C D. - 2 x 2 - 2 x 3 / 2 3 + C E. 2 ln | x | - 1 2 x + C 2. Evaluate Z 1 (3 x - 1) 4 dx . A. - 12 (3 x - 1) 5 + C B. - 1 9(3 x - 1) 3 + C C. 1 (3 x - 1) 3 + C D. - 1 3(3 x - 1) 3 + C E. - 4 (3 x - 1) 5 + C 3. Evaluate Z e 3 - 2 x dx. A. - 2 e 3 - 2 x + C B. - 1 2 e 3 - 2 x + C C. e 4 - 2 x 4 - 2 x + C D. 1 3 e 3 - 2 x + C E. e 3 - 2 x 3 - 2 x + C 4. Find a function f whose tangent line has slope x 5 - x 2 for each value of x and whose graph passes through the point (2,10). A. f ( x ) = - 1 3 (5 - x 2 ) 3 / 2 B. f ( x ) = 2 3 (5 - x 2 ) 3 / 2 + 28 3 C. f ( x ) = 1 3 (5 - x 2 ) 3 / 2 + 29 3 D. f ( x ) = - 1 3 (5 - x 2 ) 3 / 2 + 31 3 E. f ( x ) = 3 2 (5 - x 2 ) 3 / 2 + 17 2 5. Evaluate Z x ln( x 2 ) dx . A. 1 2 x 2 ln x 2 - 1 2 x 2 + C B. 1 2 x 2 ln x 2 - 1 2 x + C C. 1 2 x 2 ln x 2 - 1 6 x 3 + C D. x ln x 2 + 1 x + C E. 1 2 x 2 ln x - 1 2 x 2 + C 6. The area of the region bounded by the curves y = x 2 + 1 and y = 3 x + 5 is 7. Find the average value of f ( x ) = x 2 over the interval 1 x 4 . 8. A calculator manufacturer expects that x months from now consumers will be buying 1,000 calculators a month at a price of 20 + 3 x dollars per calculator. What is the average revenue the manufacturer can expect from the sale of calculators over the next 4 months? 9. If f ( x, y ) = ( xy + 1) 2 - p y 2 - x 2 , evaluate f ( - 2 , 1). A. 1 B. 1 - 5 C. Not defined D. - 1 - 5 E. - 1 - 3 10. A paint store carries two brands of latex paint. Sales figures indicate that if the first brand is sold for x 1 dollars per gallon and the second for x 2 dollars per gallon, the demand for the first brand will be D 1 ( x 1 , x 2 ) = 100 + 5 x 1 - 10 x 2

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224pracfinal - MA 22400 Final Exam Practice Problems The...

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