# Sp95ex1B - whichever comes first i x i f(x i f’(x i | e A...

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Sp 95 Exam 1B Name __________________ EGN 3420 SHOW ALL WORK! Problem 1 (25 pts) Consider the function f(x) = 1/x. A) Find the 3rd order truncated Taylor Series Expansion of f(x) about the pt x 0 = 1/2. B) Use the 3rd order truncated series to estimate f(x) when x = 0.6 to 3 places after the decimal point. C) Find the true per cent relative error in the answer to Part B) to 2 places after the decimal point.

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Sp 95 Exam 1B Name __________________ EGN 3420 SHOW ALL WORK! Problem 2 (25 pts) Given the function 3 16 ( ) f x x x = - use the Newton Raphson Method to fill in the table below. Round all calculations to 4 places after the decimal point, except the last column which should be rounded to 2 places after the decimal point. Stop when the magnitude of the approximate relative error is less than 1% or after 5 iterations,

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Unformatted text preview: whichever comes first. i x i f(x i ) f’(x i ) | e A | , % 1 1 2 3 4 5 Sp 95 Exam 1B Name __________________ EGN 3420 SHOW ALL WORK! Problem 3 (25 pts) The data points (0,1), (1,a), (2,5), (3,19) come from an unknown function f(x). A) Find the value of “a” if the coefficient b 3 in the Newton Divided Difference Interpolating polynomial f 3 (x) is 1. B) Find f 3 (x). The table below may help in your solution. i x i f(x i ) ∆ ∆ 2 ∆ 3 1 1 1 a 2 2 5 3 3 19 Sp 95 Exam 1B Name __________________ EGN 3420 SHOW ALL WORK! Problem 4 (25 pts) A quadratic spline fit thru the data points (1,1), (2,3), (3,6) and (4,12) is given below. 2x - 1 1 ≤ x ≤ 2 f(x) = ax 2 + bx + c 2 ≤ x ≤ 3 2x 2- 8x + 12 3 ≤ x ≤ 4 Find a, b, and c....
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Sp95ex1B - whichever comes first i x i f(x i f’(x i | e A...

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