11_Cal_Solution of Calculus_6e

# 11_Cal_Solution of Calculus_6e - because 10000r < 1 It...

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because 10000 r < 1. It follows that Chop 4 has the desired effect. C01S01.057: x 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 y 1 . 0 0 . 44 0 . 04 0 . 44 0 . 76 1 . 0 The sign change occurs between x = 0 . 2 and x = 0 . 4. x 0 . 20 0 . 25 0 . 30 0 . 35 0 . 40 y 0 . 44 0 . 3125 0 . 19 0 . 0725 0 . 04 The sign change occurs between x = 0 . 35 and x = 0 . 40. x 0 . 35 0 . 36 0 . 37 0 . 38 0 . 39 0 . 40 y 0 . 0725 0 . 0496 0 . 0269 0 . 0044 0 . 0179 0 . 04 From this point on, the data for y will be rounded. x 0 . 380 0 . 382 0 . 384 0 . 386 0 . 388 0 . 390 y 0 . 0044 0 . 0001 0 . 0045 0 . 0090 0 . 0135 0 . 0179 Answer (rounded to two places): 0 . 38. The quadratic formula yields the two roots 1 2 ( 3 ± 5 ) ; the smaller of these is approximately 0.381966011250105151795. Problems 58 through 66 are worked in the same way as Problem 57. C01S01.058: The sign change intervals are [2 , 3], [2 . 6 , 2 . 8], [2 . 60 , 2 . 64], and [2 . 616 , 2 . 624]. Answer: 1 2 ( 3 + 5 ) 2 . 62. C01S01.059: The sign change intervals are [1 , 2], [1 . 2 , 1 . 4], [1 . 20 , 1 . 24], [1 . 232 , 1 . 240], and [1 . 2352 , 1 . 2368]. Answer: 1 + 5 1 . 24. C01S01.060: The sign change intervals are [ 4 , 3], [ 3 . 4 , 3 . 2], [ 3 . 24 , 3 . 20], [ 3 . 240 , 3 . 232], and [ 3 . 2368 , 3 . 2352]. Answer: 1 5 ≈ − 3 . 24. C01S01.061: The sign change intervals are [0 , 1], [0 . 6 , 0 . 8], [0 . 68 , 0 . 72], [0 . 712 , 0 . 720], and [0 . 7184 , 0 . 7200]. Answer: 1 4 ( 7 17 ) 0 . 72. C01S01.062: The sign change intervals are [2 , 3], [2 . 6 , 2 . 8], [2 . 76 , 2 . 80], [2 . 776 , 2 . 784], and [2 . 7792 ,
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