# HW11 - Math 191 8.7 12 HW 11 Solutions 3 a n = 8 x = 3 x =...

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Math 191 HW 11 Solutions 8.7: 12 a. n = 8 Δ x = 3 8 Δ x 2 = 3 16 ; Σmf( θ i ) = 1(0)+2(0 . 09334)+2(0 . 18429)+2(0 . 27075)+2(0 . 3512)+ 2(0 . 42443) + 2(0 . 49026) + 2(0 . 58466) + 1(0 . 6) = 5 . 3977 T = 3 16 (5 . 3977) = 1 . 01207 b. n = 8 Δ x = 3 8 Δ x 3 = 1 8 ; Σmf( θ i ) = 1(0)+4(0 . 09334)+2(0 . 18429)+4(0 . 27075)+2(0 . 3512)+ 4(0 . 42443) + 2(0 . 49026) + 4(0 . 58466) + 1(0 . 6) = 8 . 14406 T = 1 8 (8 . 14406) = 1 . 01801 c. Let u = 16 + θ 2 du = 2 θdθ 1 2 du = θdθ ; θ = 0 u = 16 , θ = 3 u = 16 + 3 2 = 25; R 3 0 θ 16+ θ 2 = R 25 16 1 u ( 1 2 du ) = 1 2 R 25 16 u - 1 / 2 du = h 1 2 ± u 1 / 2 1 2 ²i 25 16 = 25 - 16 = 1; E T = R 3 0 θ 16+ θ 2 - T 1 - 1 . 01207 = - 0 . 01207; Es = R 3 0 θ 16+ θ 2 - S 1 - 1 . 01801 = - 0 . 01801 8.7: 20 a. M = 6(see Exercise 6); Then Δ x = 2 n ⇒ | E T | ≤ 2 12 ( 2 n ) 2 (6) = 4 n 2 < 10 - 4 n 2 > 4(10 4 ) n > p 4(10 4 ) = 200 , so let n = 201 b. M = 0(see Exercise 6); Then

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HW11 - Math 191 8.7 12 HW 11 Solutions 3 a n = 8 x = 3 x =...

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