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Fa98ex3 - sin = π Fa 98 EGN 3420 EXAM 3 Name Show All Work...

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Fa 98 EGN 3420 EXAM 3 Name __________________ Show All Work! Problem 1 (25 pts) The data points ( , ) x y i i in the table below are to be approximated by a second order polynomial y a a x a x = + + 0 1 2 2 . a) Find the Normal Equations which are used to solve for the least squares coefficients a a a 0 1 2 , , . x i y i y i e y y i i i = - e i 2 0 -1 1 -1 2 -1 3 2 4 7 5 15 b) Solve the Normal Equations to find the Least Squares quadratic through the data points. c) Fill in the table and find the SSE.
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Fa 98 EGN 3420 EXAM 3 Name __________________ Show All Work! Problem 2 (25 pts) a) Fit a 3rd order Newton Divided Difference polynomial f x 3 ( ) through the data points ( , ) x y i i from an unknown function f x ( ). Complete the divided-difference table below and express the coefficients b i , i=0,1,2,3 to 4 places after the decimal point. x i y f x i i = ( ) 2 3 0.0 0.0000 0.2 0.1176 0.4 0.3804 0.6 0.5706 b) Use f 3 05 ( . ) to estimate f(0.5) to 4 places after the decimal point. c) Find the true error E T (to 4 places after the decimal point) in f 3 05 ( . ) if the data points belong to the function f x x x ( )
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Unformatted text preview: sin = π . Fa 98 EGN 3420 EXAM 3 Name __________________ Show All Work! Problem 3 (25 pts) Consider the definite integral 2 1 e dx x I = ∫ a) Numerical integration using n = 10 intervals is to be used to approximate I. Fill in the table below where f x ( ) is the integrand, i.e. the function being integrated. i x i f i = f ( x i ) 1.0000 1.0000 1 2 3 4 5 6 7 8 9 10 7.3891 b) Use Trapezoidal Integration to estimate I. c) Use Simpson’s Formula to estimate I. Round all calculations to 4 places after the decimal point. Fa 98 EGN 3420 EXAM 3 Name __________________ Show All Work! Problem 4 (25 pts) Fit a saturation growth curve to the ( , ) x y i i data below. Use the table for intermediate calculations. Round all results to 4 places after the decimal point. x i y i u i z i u i 2 u z i i 0.5000 0.3000 1.0000 0.5000 2.0000 0.9000 5.0000 1.2000 10.0000 1.5000 25.0000 1.8000...
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