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

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4.6 Pages 269-270 # 1, 3 (trapezoidal, parametric, and exact), 11, 13, 15, 27, 28, 29 2 13 1 ( ) ; 0.25 8 fx h x == = 0 1.00 x = 0 ()1 = 1 1.25 x = 1 ( ) 0.64 = 2 1.50 x = 2 ()0 . 4 4 4 4 3 1.75 x = 3 ( ) 0.3265 4 2.00 x = 4 . 2 5 = 5 2.25 x = 5 ( ) 0.1975 6 2.50 x = 6 ( ) 0.16 = 7 2.75 x = 7 . 1 3 2 2 8 3.00 x = 8 ( ) 0.1111 1. Trapezoidal Rule: 3 01 7 8 2 1 1 0.25 [ ( ) 2 ( ) 2 ( ) ( )] 0.6766 2 d x x ≈+ + + + Parabolic Rule: 3 012 7 8 2 1 1 0.25 [ ( ) 4 ( ) 2 ( ) 4 ( ) ( )] 0.6671 3 d x x + + + + Fundamental Theorem of Calculus: 3 3 2 1 1 11 1 2 1 0.6667 33 dx x x  + =   2–0 ( ) 0.25 8 xh = 0 0.00 x = 0 = 1 0.25 x = 1 () 0 . 5 = 2 0.50 x = 2 ( ) 0.7071 3 0.75 x = 3 ( ) 0.8660 4 1.00 x = 4 = 5 1.25 x = 5 ( ) 1.1180 6 1.50 x = 6 ( ) 1.2247 7 1.75 x = 7 ( ) 1.3229 8 2.00 x = 8 ( ) 1.4142 3. Trapezoidal Rule: 2 7 8 0 0.25 [ ( ) 2 ( ) 2 ( ) ( )] 1.8615 2 xdx f x + + + Parabolic Rule: 2 123 7 8 0 0.25 [ ( ) 4 ( ) 2 ( ) 4 ( ) ( )] 1.8755 3 + + + + Fundamental Theorem of Calculus: 2 2 3/2 0 0 24 2 1.8856 x 11. () 23 12 ; x x ′′ =− = The largest that f c can be on [ ] 1, 3 occurs when 1 c = , and ( ) f = 3 2 31 400 20 . 0 1 ; 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 d x fx x ≈+ + + + " 13. () 3/2 11 ; 2 4 x x ′′ == The largest that f c can be on [ ] 1, 4 occurs when 1 c = , and 1 1 4 f = . 3 2 41 1 900 0.01; 6 12 n n  ≤≥   Round up: n = 8 4 01 7 8 1 0.375 [ ( ) 2 ( ) 2 ( ) ( )] 4.6637 2 xdx f x + + + " 15. 4 23 4 5 12 6 2 4 ;; ; f x x xx x ′′′ =− = = The largest that ( ) 4 f c can be on [ ] 1, 3 occurs when 1 c = , and ( ) 4 4 f = . 5 4 24 4.545 180 n n ≤≈ Round up to even:
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This note was uploaded on 02/25/2010 for the course MATH 201 taught by Professor Kim during the Spring '07 term at SIU Carbondale.

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

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