A n 8 21 a 78 b 7 1 0 23 f 4 x 0 for all x

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Unformatted text preview: 15. (a) n ≥ 238 (b) n ≥ 10 17. (a) n ≥ 51 (b) n ≥ 4 19. (a) n ≥ 37 (b) n ≥ 3 13. (a) n ≥ 8 21. (a) 78 (b) 7 1 0 23. f (4) (x) = 0 for all x; therefore by (8.7.3) the theoretical error is zero 1 1 3 T −= = E2 8 3 24 (b) S1 − 0 b a 1 25. (a) T2 − x2 dx = x4 dx = 1 1 5 S −= = E1 24 5 120 29. (a) 49. 4578 (b) 1280.56 31. error ≤ 4. 01 × 10−7 27. Using the hint, Mn = area ABCD = area AEFD ≤ 1 f (x) dx ≤ Tn . 33. 0 4 dx = 4 tan−1 x 1 + x2 1 0 =4 π 4 −0 =π 3. 14159 (a) 3.14141 (b) 3.14159 SECTION 8.8 1. y1 is; y2 is not 11. y = x + C e2x 23. y = 2 e−x + x − 1 3. y1 and y2 are solutions 13. y = 2 3 5. y1 and y2 are solutions 15. y = C ee x 7. y = − 1 + C e2x 2 9. y = 2 2 5 + C e−(5/2)x 21. y = C (x + 1)−2 nx + Cx4 17. y = 1 + C (e−x + 1) 27. y = x2 (ex − e) 19. y = e−x 12 x 2 +C 25. y = e−x ln(1 + ex ) + e − ln 2 29. y = C1 ex + C2 x ex 41. (a) 200 ( 4 )t /5 5 (b) 200 2 ( 4 )t /25 5 35. T (1) ∼ 40. 10◦ ; 1. 62 min = dP = k (M − P ) dt (b) P (t ) = M (1 − e−0.0357t ) (c) 65 days 37. (a) v(t )...
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