ma441f07ex3sol

# ma441f07ex3sol - Dr. H. Khanal Spring 2008 MA 441.01 Sample...

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Dr. H. Khanal Spring 2008 MA 441.01 Sample Test #3 (SOLUTION) ! Read each problem carefully before attempting a solution. Show all work to justify your answers. Answer alone carries no credit. Partial credit only for signiﬁcant progress towards a correct solution. Box or underline ﬁnal answers. Problems. 1 . [12] Determine which functions below are periodic. For those that are, ﬁnd the function’s fundamental period (smallest positive period) or indicate if it does not exist. (i) f ( x ) = cos 3 x (ii) f ( x ) = | sin x | (iii) f ( x ) = 2 π (i) periodic, p = 2 3 π . (ii) periodic, p = π . (iii) periodic, the fundamental period p does not exist. 2 . [12] Determine whether the given function is even, odd, or neither. (i) f ( x ) = x 3 + sin2 x (ii) f ( x ) = e x - e - x (iii) The function f that is π -periodic with f ( x ) = sin x for 0 x π . (i) odd: f ( - x ) = ( - x ) 3 + sin(2( - x )) = - x 3 - sin2 x = - f ( x ) (ii) odd: f ( - x ) = e ( - x ) - e ( - ( - x )) = e - x - e x = - f ( x ) (iii) even: f is π -periodic. Drawing picture helps to see symmetry about the

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## This note was uploaded on 06/03/2008 for the course MA 441 taught by Professor Kaba during the Fall '08 term at Embry-Riddle FL/AZ.

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ma441f07ex3sol - Dr. H. Khanal Spring 2008 MA 441.01 Sample...

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