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M116ExFF11

# M116ExFF11 - Math 116 Final Exam Name Instructor Section 1...

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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
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M116ExFF11 - Math 116 Final Exam Name Instructor Section 1...

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