Pre-Calc Homework Solutions 226

Pre-Calc Homework Solutions 226 - 226 Section 5.5 4 4 0 5....

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Unformatted text preview: 226 Section 5.5 4 4 0 5. (a) f (x) x f (x) 1 (0 2 x, h 0 0 1 1 1 3 2 3 2) 2( 1 3/2 x 4 10. (a) f (x) 4 2 S 3 x3 1 1 2x, h 0 0 4(0) 3 ( 1) 4 1 3 21 2 x f (x) 2) 5.146 (b) 1 (1 3 1 1 2( 1) 1 4 x 4 81 4 2 4 T (b) f (x) 2(1) 2( 3) 4(4) x2 9 3 1 21) 12 1 1/2 x , f (x) 2 0 on [0, 4] (x 3 2x) dx 1 The approximation is an underestimate. 4 1 4 1 (c) 0 x dx 2 3/2 x 3 4 0 16 3 0 4 4 3 4 5.333 Es 0 x3 12 (c) For f (x) 2x, Mf (4) 0 since f (4) 0. 6. (a) f (x) x f (x) sin x, h 0 0 4 2 2 2 (d) Simpson's Rule for cubic polynomials will always give exact values since f (4) 0 for all cubic polynomials. 0 2 2 1 2 2 11. The average of the 13 discrete temperatures gives equal weight to the low values at the end. 0 1.896 12. (a) 1 (126 2 T (b) f (x) 8 0 2 2 2 2(1) sin x 2 2 65 1 12 2 66 70.08 ... 2 58 110) 841 cos x, f (x) 0 on [0, ] av( f) 841 The approximation is an underestimate. (c) 0 sin x dx 2(8.2) 15,990 ft3 cos x 0 2 ... 2(12.7) 13.0)(30) (b) We are approximating the area under the temperature graph. By doubling the endpoints, the error in the first and last trapezoids increases. 13. S50 14. S50 3.13791, S100 1.08943, S100 3.14029 1.08943 1.37066 using a 1.37076 using a 0.82812 0.0001 as lower 0.000000001 as 7. 5 (6.0 2 2(9.1) 200 8. (a) (0 2 2(520) 0)(20) 2(800) 2(1000) ... 2(860) 15. S50 1.37066, S100 limit S50 1.37076, S100 lower limit 16. S50 0.82812, S100 26,360,000 ft3 (b) You plan to start with 26,360 fish. You intend to have (0.75)(26,360) 19,770 20 17. (a) T10 1.983523538 T100 1.999835504 T1000 1.999998355 (b) n 10 100 1000 (c) ET 10 2 19,770 fish to be caught. Since ET 0.016476462 2 Tn 10 2 988.5, the town can sell at most 988 licenses. 1 to change seconds 3600 1.6476462 10 10 6 4 1.64496 1.645 ET 9. Sum the trapezoids and multiply by to hours 1 (2.2(0 2 30) (3.2 2.2)(30 50) 70) 90) 110) 120) 130)) (5.9 (10.2 40) 4.5)(50 7.8)(70 60) 80) 100) 10n n 2 (4.5 (7.8 (12.7 (20.6 (26.2 (37.1 3.2)(40 5.9)(60 10.2)(80 (d) b ET ET n a , h2 2 ,M n2 3 12n 2 1 (16.0 12.7)(90 12 n 2 3 16.0)(100 20.6)(110 26.2)(120 10n 12(10n)2 10 2 ET n 1 3600 0.9785 miles ...
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