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# Fa00ex1 - EGN 3420 Fa 2000 Exam I Name SHOW ALL WORK...

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EGN 3420 Exam I Name_____________ Fa 2000 SHOW ALL WORK! Problem 1 (30pts) For the function sin ( ) x f x x = shown below. a) Find f 2 ( x ), the second order truncated Taylor Series expansion of f ( x ) about x 0 = π . b) Use f 2 ( x ) to approximate f (0). c) Defining f (0) as sin ( ) 0 0 x Lim f x Lim x x x = Use L'Hopital's rule to find f (0) and the true error E T at x =0. -6 -4 -2 0 2 4 6 -0.5 0 0.5 1 1.5 π x (rad) y f(x)=sin(x)/x vs, x

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EGN 3420 Exam I Name_____________ Fa 2000 SHOW ALL WORK! Problem 2 (25pts) The function sin ( ) x f x x = has a root located between 2 and 4. Fill in the table below for the first three iterations of the Bisection Method. Express all answers to four digits after the decimal point. Iteration x l x u x r f ( x l ) f ( x r ) e A, % e T , % 1 2.0000 4.0000

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Fa00ex1 - EGN 3420 Fa 2000 Exam I Name SHOW ALL WORK...

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