dev22384 - f i = f x i for some unknown function f(0 5 2...

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MAT 2384-Fall 2009-Assignment #2 To be submitted in class on Friday, October 2 Question 1. Solve each of the initial value problems: 1. ( y cos( x + y )) dx + (3 sin( x + y ) + y cos( x + y )) dy = 0 , y (0) = π 2 2. y 0 = - y x + x, y (1) = 2 . 3. y 0 - 3 y = e 2 x , y (0) = 0 4. y 0 + 2 x y = x y , y (1) = 2 5. y 0 - 2 y x = - x 2 y 2 , y (1) = 5 Question 2. 1. Use the Secant Method to estimate 15 to 7 decimal places. Start with x 0 = 3, x 1 = 4. 2. Consider the data points ( x i , f i ), i = 0 , 1 , 2 where
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Unformatted text preview: f i = f ( x i ) for some unknown function f : (0 . 5 , 2 . 2), (0 . 75 , 1 . 78) and (1 . 4 , 1 . 51). Find p 2 ( x ) with coeﬃcients to 4 decimal places via Lagrange Interpolation . Interpolate a value at x = 0 . 9. Given that 2 3 ≤ f 000 ( x ) ≤ 5 2 on [0 . 5 , 1 . 4], estimate the error bounds. 1...
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