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2 x dx. Evaluate x 2x3/2 1 2 2 +C A. ln |x| + C B. 2 1/2 + C C. 2 ln |x| x 3 x 2x 2 2x3/2 1 + C E. 2 ln |x| + C D. 2 x 3 2x 2. Evaluate 1 dx. (3x...

Question 4,5,15,16,21,31,32,33

MA 22400 Final Exam Practice Problems The Formula Page (available on the course web site) will be attached to the fnal exam. 1. Evaluate i p 2 x - x P 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 i 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 i 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 ±unction f whose tangent line has slope x 5 - x 2 ±or each value o± 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 i 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 o± the region bounded by the curves y = x 2 + 1 and y = 3 x + 5 is A. 125 6 B. 56 3 C. 27 2 D. 25 6 E. 32 3 7. Find the average value o± f ( x ) = x 2 over the interval 1 x 4 . A. 17 2 B. 15 2 C. 21 D. 65 3 E. 7 8. A calculator manu±acturer expects that x months ±rom now consumers will be buying 1,000 calculators a month at a price o± 20+3 x dollars per calculator. What is the average revenue the manu±acturer can expect ±rom the sale o± calculators over the next 4 months? A. $8,000 B. $16,000 C. $24,000 D. $96,000 E. $6,500 9. I± f ( x, y ) = ( xy + 1) 2 - r y 2 - x 2 , evaluate f ( - 2 , 1). A. 1 B. 1 - 5 C. Not defned D. - 1 - 5 E. - 1 - 3 10. A paint store carries two brands o± latex paint. Sales fgures indicate that i± the frst brand is sold ±or x 1 dollars per gallon and the second ±or x 2 dollars per gallon, the demand ±or the frst brand will be D 1 ( x 1 , x 2 ) = 100 + 5 x 1 - 10 x 2 gallons per month and the demand ±or the second brand will be D 2 ( x 1 , x 2 ) = 200 - 10 x 1 + 15 x 2 gallons per month. Express the paint store’s total monthly revenue, R , as a ±unction o± x 1 and x 2 . A. R = x 1 D 1 ( x 1 , x 2 ) + x 2 D 2 ( x 1 , x 2 ) B. R = D 1 ( x 1 , x 2 ) + D 2 ( x 1 , x 2 ) C. R = D 1 ( x 1 , x 2 ) D 2 ( x 1 , x 2 ) D. R = x 2 D ( x 1 , x 2 )+ x 1 D 2 ( x 1 , x 2 ) E. R = x 1 x 2 + D 1 ( x 1 , x 2 ) D 2 ( x 1 , x 2 ) 1
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MA 22400 Final Exam Practice Problems 11. Compute ∂z ∂x , where z = ln( xy ). A. 1 x B. 1 y C. 1 xy D. 1 x + 1 y E. y x 12. Compute f uv if f = uv + e u +2 v . A. 0 B. u + 2 e u +2 v C. v + 2 e u +2 v D. 1 + 2 e u +2 v E. 1 + e u +2 v 13. Find and classify the critical points of f ( x, y ) = ( x - 2) 2 + 2 y 3 - 6 y 2 - 18 y + 7. A. (2,3) saddle point; (2, - 1) relative minimum B. (2,3) relative maximum; (2, - 1) relative minimum C. (2,3) relative minimum; (2, - 1) relative maximum D. (2,3) relative maximum; (2, - 1) saddle point E. (2,3) relative minimum; (2, - 1) saddle point 14. A manufacturer sells two brands of foot powder, brand A and brand B. When the price of A is x cents per can and the price of B is y cents per can the manufacturer sells 40 - 8 x + 5 y thousand cans of A and 50 + 9 x - 7 y thousand cans of B. The cost to produce A is 10 cents per can and the cost to produce B is 20 cents per can. Determine the selling price of brand A which will maximize the pro±t. A. 40 cents B. 45 cents C. 15 cents D. 50 cents E. 35 cents 15. Use increments to estimate the change in z at (1,3) if ∂z ∂x = 2 x - 4 , ∂z ∂y = 2 y + 7, the change in x is 0.3 and the change in y is 0.5. A. 7.1 B. 2.9 C. 4.9 D. 5.9 E. 6.3 16. Using x worker-hours of skilled labor and y worker-hours of unskilled labor, a manufacturer can produce f ( x, y ) = x 2 y units. Currently 16 worker-hours of skilled labor and 32 worker-hours of unskilled labor are used. If the manufacturer increases the unskilled labor by 10 worker-hours, use calculus to estimate the corresponding change that the manufacturer should make in the level of skilled labor so that the total output will remain the same. A. Reduce by 4 hours. B. Reduce by 10 hours. C. Reduce by 5 4 hours. D. Reduce by 5 2 hours. E. Reduce by 5 hours. 17. Find the maximum value of the function f ( x, y ) = 20 x 3 / 2 y subject to the constraint x + y = 60. Round your answer to the nearest integer. A. 84,654 B. 188,334 C. 4,320 D. 259,200 E. 103,680 18. Evaluate i 2 1 i 1 0 (2 x + y ) dydx. A. 9 2 B. 5 2 C. 3 2 D. 7 2 E. 1 2 19. The general solution of the di²erential equation dy dx = 2 y + 1 is: A. x = y 2 + y + C B. 2 y + 1 = Ce 2 x C. y = 2 xy + x + C D. y = Ce 2 x - 2 y - 1 E. y = Ce 2 x 2
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