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# Sp98ex1 - Sp 98 EGN 3420 Exam 1 Name DO ANY 3 PROBLEMS...

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Sp 98 EGN 3420 Exam 1 Name__________________ DO ANY 3 PROBLEMS Check the 3 problems you want graded: 1. 2. 3. 4. Problem 1 (45 pts) The function f(x) = cos(x) is expanded in a 1 st order truncated series about the pt x=a. f 1 (x) = f(a) +f’(a)(x-a) The point “a” is chosen so that f 1 ( π ) = 0. (see graph) a π f(x)=cos(x) and f 1 (x) expanded about x=a f 1 (x) f(x) = cos(x)

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a) Show that “a” is a root of f(a) = ( π -a) tan(a) - 1 = 0. Hint: tan( ) sin( ) cos( ) a a a = b) Try to find the root by doing 5 iterations of the Simple One Point Iteration Method starting with an initial guess of a 0 = 1. Use the table below to enter your results (4 places after the decimal point). Be sure to show how you found g(a) and comment on whether the method appears to be converging. i a i a i+1 =g(a i ) 0 1 1 2 3 4 5 c) Try to find the root by doing 3 iterations of the Newton-Raphson Method starting with an initial guess of a 0 = 1. Use the table below to enter your results (4 places after the decimal point). Is the method converging?
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Sp98ex1 - Sp 98 EGN 3420 Exam 1 Name DO ANY 3 PROBLEMS...

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