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# hw46 - 4.6 Pages 269-270 1 3(trapezoidal parametric and...

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4.6 Pages 269-270 # 1, 3 (trapezoidal, parametric, and exact), 11, 13, 15, 27, 28, 29 2 1 3 –1 ( ) ; 0.25 8 f x h x = = = 0 1.00 x = 0 ( ) 1 f x = 1 1.25 x = 1 ( ) 0.64 f x = 2 1.50 x = 2 ( ) 0.4444 f x 3 1.75 x = 3 ( ) 0.3265 f x 4 2.00 x = 4 ( ) 0.25 f x = 5 2.25 x = 5 ( ) 0.1975 f x 6 2.50 x = 6 ( ) 0.16 f x = 7 2.75 x = 7 ( ) 0.1322 f x 8 3.00 x = 8 ( ) 0.1111 f x 1. Trapezoidal Rule: 3 0 1 7 8 2 1 1 0.25 [ ( ) 2 ( ) 2 ( ) ( )] 0.6766 2 dx f x f x f x f x x + +…+ + Parabolic Rule: 3 0 1 2 7 8 2 1 1 0.25 [ ( ) 4 ( ) 2 ( ) 4 ( ) ( )] 0.6671 3 dx f x f x f x f x f x x + + +…+ + Fundamental Theorem of Calculus: 3 3 2 1 1 1 1 1 2 1 0.6667 3 3 dx x x = = + = 2 – 0 ( ) ; 0.25 8 f x x h = = = 0 0.00 x = 0 ( ) 0 f x = 1 0.25 x = 1 ( ) 0.5 f x = 2 0.50 x = 2 ( ) 0.7071 f x 3 0.75 x = 3 ( ) 0.8660 f x 4 1.00 x = 4 ( ) 1 f x = 5 1.25 x = 5 ( ) 1.1180 f x 6 1.50 x = 6 ( ) 1.2247 f x 7 1.75 x = 7 ( ) 1.3229 f x 8 2.00 x = 8 ( ) 1.4142 f x 3. Trapezoidal Rule: 2 0 1 7 8 0 0.25 [ ( ) 2 ( ) 2 ( ) ( )] 1.8615 2 xdx f x f x f x f x + +…+ + Parabolic Rule: 2 1 2 3 7 8 0 0.25 [ ( ) 4 ( ) 2 ( ) 4 ( ) ( )] 1.8755 3 xdx f x f x f x f x f x + + +…+ + Fundamental Theorem of Calculus: 2 2 3/2 0 0 2 4 2 1.8856 3 3 xdx x = = 11. ( ) ( ) 2 3 1 2 ; f x f x x x ′′ = − = The largest that ( ) f c ′′ can be on [ ] 1,3 occurs when 1 c = , and ( ) 1 2 f ′′ = ( ) ( ) 3 2 3 1 400 2 0.01; 3 12 n n Round up: n = 12

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3 0 1 11 12 1 1 0.167 [ ( ) 2 ( ) 2 ( ) ( )] 1.1007 2 dx f x f x f x f x x + + + + " 13. ( ) ( ) 3/ 2 1 1 ; 2 4 f x f x x x ′′ = = − The largest that ( ) f c ′′ can be on [ ] 1,4 occurs when 1 c = , and ( ) 1 1 4 f ′′ = . ( ) 3 2 4 1 1 900 0.01; 4 16 12 n n Round up: n = 8 4 0 1 7 8 1 0.375 [ ( ) 2 ( ) 2 ( ) ( )] 4.6637 2 x dx f x f x f x
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hw46 - 4.6 Pages 269-270 1 3(trapezoidal parametric and...

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