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# Sp95ex1A - Do not round the results of intermediate...

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Sp 95 Exam 1A Name __________________ EGN 3420 SHOW ALL WORK! Problem 1 (25 pts) Consider the function f(x) = x 10 - 1. A) Find an expression for the 2nd order truncated Taylor Series Expansion f 2 (x) evaluated at x=1.01x 0 , where x 0 is the point at which the series is expanded about. Leave your simplified answer in terms of x 0 . Numeric constants should be rounded to 5 places after the decimal point. B) If x 0 =1, find the true relative error, as a per cent, in f 2 (1.01x 0 ). C) If x 0 =1, find f 3 (1.01x 0 ). In Parts B) and C) express your answer rounded to 5 places after the decimal point.

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Sp 95 Exam 1A Name __________________ EGN 3420 SHOW ALL WORK! Problem 2 (25 pts) Use the simple one point iteration method to find the root of f(x) = x - ln(x 2 + 2) = 0 Start with x 0 = 0 and fill in the table below. Round all entries in the table to 4 places after the decimal point.

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Unformatted text preview: Do not round the results of intermediate calculations. i x i f(x i ) 1 2 5 10 Sp 95 Exam 1A Name __________________ EGN 3420 SHOW ALL WORK! Problem 3 (25 pts) Complete the first four iterations of the Bisection Method to find the positive root of 4 ( ) 16 f x x =-. Complete the table below. Round all answers to 4 places after the decimal point. x L x U x R e T , % 5 Sp 95 Exam 1A Name __________________ EGN 3420 SHOW ALL WORK! Problem 4 (25 pts) A) Complete the table below to find the coefficients of the Newton Divided Difference 3rd order interpolating polynomial, i.e. f 3 (x) = b + b 1 (x-x ) + b 2 (x-x )(x-x 1 ) + b 3 (x-x )(x-x 1 )(x-x) i x i f(x i ) ∆ ∆ 2 ∆ 3-1 1 2 1 2 3 3.5 3 4 7 B) Use f 3 (x) to estimate f(1)....
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Sp95ex1A - Do not round the results of intermediate...

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