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Z 2 − 2z − 54 = 0 x2 − 6x + 5 = 0 12. 9x2 − 12x + 4 = 0 11. 3 2 Factor the polynomials in Exercises 13–30. 19. 30 − 4x − 2x2 20. 15 + 12x − 3x2 21. 3x − x2 22. 4x2 − 1 23. 6x − 2x3 24. 16x + 6x2 − x3 25. x3 − 1 26. x3 + 125 27. 8x + 27 28. x3 − 29. x2 − 14x + 49 30. x2 + x + 3 1 8 1 4 Find the points of intersection of the pairs of curves in Exercises 31–38. 31. y = 2x2 − 5x − 6, y = 3x + 4 32. y = x2 − 10x + 9, y = x − 9 13. x2 + 8x + 15 14. x2 − 10x + 16 33. y = x2 − 4x + 4, y = 12 + 2x − x2 15.

06)n . In this example, the interest period was 1 year. 06). 06, the compound amount will grow by a factor of (1 + i) at the end of each interest period. If a principal amount P is invested at a compound interest rate i per interest period, for a total of n interest periods, the compound amount A at the end of the nth period will be A = P (1 + i)n . EXAMPLE 5 SOLUTION (1) Compound Interest If $5000 is invested at 8% per year, with interest compounded annually, what is the compound amount after 3 years?

61/3 · 62/3 41. (xy)6 x4 y2 x x3 y −2 √ √ 3 59. 3 x · x2 √ Let f (x) = 3 x and g(x) = Take x > 0. In Exercises 41–70, use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. 47. 69. √ 54. 3 3x2 2y 1 64. yx−5 −3x 15x4 x−4 57. 3 x 53. (2x)4 56. 58. (−3x)3 67. In Exercises 29–40, use the laws of exponents to compute the numbers. 29. 51/3 · 2001/3 −x3 y −xy 61. 28. 1−1 . 2 1/3 39 3 78. f (x)g(x) 81. f (f (x)) g(x) f (x) f (x) g(x) 79.

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Calculus & Its Applications by Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar


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