Su95ex1 - α L = 0.5 and α U = 1.0. Complete 3 iterations...

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Su 95 EGN 3420 EXAM 1 Name ___________________ SHOW ALL WORK Problem 1 (30 pts) A) Find f 2 (x), the second order truncated Taylor Series Expansion of the function f x e x x ( ) sin = - about the point x 0 . Leave your answer in terms of x and x 0 . B) If x 0 = π /2, then the quadratic function f 2 (x) can be expressed as f x a a x a x 2 0 1 2 2 ( ) = + + where a a a 0 1 2 , , and are constants. Find a a a 0 1 2 , , and and leave your answers in terms of π .
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Su 95 EGN 3420 EXAM 1 Name ___________________ SHOW ALL WORK! Problem 2 (35 pts) A cantilevered beam extending from its clamped end (x=0) to its free end (x=L) has a maximum deflection δ max at the end of the beam, i.e. at x=L. The deflection δ at location x= α L (0< α <1) is related to δ max by the equation f( ) / max α α α α δ δ = - + - = 4 3 2 4 6 3 0 Use the Bisection Method to solve for the value of α at which δ / δ max is equal to 0.75. Start with an initial bracket of
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Unformatted text preview: α L = 0.5 and α U = 1.0. Complete 3 iterations and fill in the table below. Round all answers to 5 places after the decimal point. i α L α U α R A e 0.50000 1.00000 1 2 3 Su 95 EGN 3420 EXAM 1 Name ___________________ SHOW ALL WORK! Problem 3 (30 pts) Use the Newton-Raphson Method to find the value of x where the linear function y x = + 1 2 and the trigonometric function y=cos(x) are equal. Start with an initial guess of x = 0. Fill in the table below and round the answers for x i and x i+1 to 4 places after the decimal point. Use the rounded answers for x i to calculate x i+1 . Stop when there is no change in x i (rounded to 4 places after the decimal point). i x i f(x i ) f’(x i ) x i+1 1 2 3 4 5 6...
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This note was uploaded on 06/09/2011 for the course EGM 4320 taught by Professor Klee during the Spring '11 term at University of Central Florida.

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Su95ex1 - α L = 0.5 and α U = 1.0. Complete 3 iterations...

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