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Tutorial_0_-_Essential_Math_for_ECON2003

# Tutorial_0_-_Essential_Math_for_ECON2003 - Intermediate...

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1 Intermediate Macroeconomics Tutorial 0 Math Review Simplify 1. p 7 p 3 . 2. a 5 b 3 a 4 b 6 . 3. p 5 q 3 s 4 p 8 q 5 s 2 . 4. q 15 q 13 . 5. p 3 q 15 pq 13 . 6. m 6 n 5 m 5 n 2 . 7. l 3 m 5 n 2 lm 3 n. Simplify 8. (p 4 ) 5 . 9. (x 2 y 3 ) 3 . 10. (p 5 q 2 ) 6 . 11. 2 5 3 3 5 x y . 12. 2 7 5 4 9 p q 13. 4 5 3 5 9 r s Rewrite using positive indices only: 14. 5 -4 . 15. 7 -5 . 16. x -3 . 17. y -2 .

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2 Rewrite using negative indices only: 18. 4 1 x . 19. 7 1 a . 20. 9 1 m . Rewrite using surds: 21. 3 1/2 22. 7 1/3 23. (-19) 1/3 24. 2 -1/2 25. (3/4) -1/4 Rewrite in exponent form: 26. 12 27. 3 7 28. 4 20 29. 1 40 30. 3 2 30 60 Differentiate with respect to x: 31. 5 ( 1) x 32. 2 ln( 1) x 33. 1 ( 1) x 34. 1 1 x x 35. ln( ) x x 36. ln( ) ln( 1) x x 37. 1 2 2 ( 1) x x
3 38. Suppose a consumer has the following utility function 1/3 2/3 ( , ) = U X Y X Y . Further suppose that his income is \$450 and that 7 x P and 4 y P . Calculate Troy’s optimal consumption of X and Y.

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Tutorial_0_-_Essential_Math_for_ECON2003 - Intermediate...

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