finpract - Practice problems for the Final, part 3 Note:...

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Unformatted text preview: Practice problems for the Final, part 3 Note: Practice problems for the Final Exam, part 1 and part 2 are the same as Practice problems for Midterm 1 and Midterm 2. 1. Calculate Fourier Series for the function f ( x ), defined on [- 2 , 2], where f ( x ) = (- 1 ,- 2 x , 2 , < x 2 . 2. Calculate Fourier Series for the function f ( x ), defined on [- 5 , 5], where f ( x ) = 3 H ( x- 2) . 3. Calculate Fourier Series for the function, f ( x ), defined as follows: (a) x [- 4 , 4], and f ( x ) = 5 . (b) x [- , ], and f ( x ) = 21 + 2sin5 x + 8cos2 x. (c) x [- , ], and f ( x ) = 8 X n =1 c n sin nx, with c n = 1 /n. (d) x [- 3 , 3], and f ( x ) =- 4 + 6 X n =1 c n (sin( nx/ 3) + 7cos( nx/ 3)) , with c n = (- 1) n . 4. (a) Let f ( x ) = x + x 3 for x [0 , ]. What coefficients of the Fourier Series of f are zero? Which ones are non-zero? Why? (b) Let g ( x ) = cos( x 5 )+sin( x 2 ). What coefficients of the Fourier Series of g are zero? Which ones are non-zero? Why? 1 5. Let f ( x ) = 2 x + x 4 for x [0 , 5]. (a) Write down the function G ( x ), which is the odd continuation for f ( x ). Specify what terms will be zero and non-zero in the Fourier expansion for G ( x )....
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finpract - Practice problems for the Final, part 3 Note:...

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