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Pre-Calc Homework Solutions 58

# Pre-Calc Homework Solutions 58 - \$36,500(1.035 for the...

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34. One possible answer: Assume y 5 x and y 5 1 are continuous. Use the product, difference, and quotient theorems. One also needs to verify that the limit of this function as x approaches 1 is 2. Alternately, observe that the function is equivalent to y 5 x 1 1 (for all x ), which is continuous by the sum theorem. Domain: ( 2‘ , ) 35. One possible answer: 36. One possible answer: 37. One possible answer: 38. One possible answer: 39. [ 2 3, 3] by [ 2 2, 2] Solving x 5 x 4 2 1, we obtain the solutions x < 2 0.724 and x < 1.221. 40. [ 2 6, 6] by [ 2 4, 4] Solving x 5 x 3 1 2, we obtain the solution x < 2 1.521. 41. We require that lim x 3 1 2 ax 5 lim x 3 2 ( x 2 2 1): 2 a (3) 5 3 2 2 1 6 a 5 8 a 5 } 4 3 } 42. Consider f ( x ) 5 x 2 e 2 x . f is continuous, f (0) 5 2 1, and f (1) 5 1 2 } 1 e } . 0.5. By the Intermediate Value Theorem, for some c in (0, 1), f ( c ) 5 0 and e 2 c 5 c . 43. (a) Sarah’s salary is \$36,500 5 \$36,500(1.035)
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Unformatted text preview: \$36,500(1.035) for the first year (0 # t , 1), \$36,500(1.035) for the second year (1 # t , 2), \$36,500(1.035) 2 for the third year (2 # t , 3), and so on. This corresponds to y 5 36,500(1.035) int t . (b) [0, 4.98] by [35,000, 45,000] The function is continuous at all points in the domain [0, 5) except at t 5 1, 2, 3, 4. 44. (a) We require: f ( x ) 5 { This may be written more compactly as f ( x ) 5 5 0 # x # 6 6 , x # 24 2 1.10 int( 2 x ), 7.25, x 5 0 , x # 1 1 , x # 2 2 , x # 3 3 , x # 4 4 , x # 5 5 , x # 6 6 , x # 24. 1.10, 2.20, 3.30, 4.40, 5.50, 6.60, 7.25, y x 5 5 y = f ( x ) y x 5 5 y = f ( x ) y x 5 5 y = f ( x ) y x 5 5 y = f ( x ) 58 Section 2.3...
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