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ME 303 Practice Quiz1

# ME 303 Practice Quiz1 - S Kalnaus Fall 2008 ME 303...

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1 S. Kalnaus Fall 2008 ME 303 Numerical Methods September 15, 2008 Quiz 1 Name:____ SOLUTION __________________ Note: Write all the steps leading to the answer (unless a question is of a multiple choice type). No books or notes are allowed during the quiz. The duration of quiz is 30 min. 1. (8 pts) Represent the function ) cos( ) ( x x f = , as Taylor series with center 0 0 = x . Express your result as a formula showing the summation over infinite number of terms = 0 n General form of Taylor series: = = 0 0 0 ) ( ! ) )( ( ) ( n n n x x x f x f )! 2 ( ) 1 ( ! 4 ! 2 1 ) cos( 1 ) 0 cos( ) ( 0 ) 0 sin( ) ( 1 ) 0 cos( ) ( 0 ) 0 sin( ) ( 1 ) 0 cos( ) ( 0 2 0 4 2 0 0 0 0 0 0 n x x x x x f x f x f x f x f x n n n IV = = + = = = = = = = = = = = = K M 2. (1 pt) Circle the correct answer. By representing a Taylor series as a Taylor polynomial with finite number of terms we introduce: a) Round-off error; b) Truncation error 3. (1 pt) If 0 ) det( = A then the matrix A is called: a) singular b) ill-conditioned 4. (2 pts) Consider the following matrix: = 16 1 7 5 2 14 1 0 0 D Is this matrix singular? Explain your answer. 0

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ME 303 Practice Quiz1 - S Kalnaus Fall 2008 ME 303...

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