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ExamFinalW11P

# ExamFinalW11P - Math 116 Final Exam April 2011 Name...

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Math 116 / Final (April 2011) page 2 You may find the following expressions useful. And you may not. But you may use them if they prove useful. “Known” Taylor series (all around x = 0 ): sin( x ) = x - x 3 3! + · · · + ( - 1) n x 2 n +1 (2 n + 1)! + · · · · · · for all values of x cos( x ) = 1 - x 2 2! + · · · + ( - 1) n x 2 n (2 n )! + · · · for all values of x e x = 1 + x + x 2 2! + · · · + x n n ! + · · · for all values of x ln(1 + x ) = x - x 2 2 + x 3 3 - x 4 4 + · · · + ( - 1) n +1 x n n + · · · for - 1 < x < 1 (1 + x ) p = 1 + px + p ( p - 1) 2! x 2 + p ( p - 1)( p - 2) 3! x 3 + · · · for - 1 < x < 1
Math 116 / Final (April 2011) page 3 1 . [10 points] For each question, circle if the statement is always true or false. No justi- fication is necessary .

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ExamFinalW11P - Math 116 Final Exam April 2011 Name...

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