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formulasheet - x with | x |< 1(1 x p = 1 ∞ X n =1 p p-1...

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Formulas which you may use freely without reference: The Taylor series T ( x ) for f ( x ) centered at a is given by T ( x ) = X n =0 f ( n ) ( a ) n ! ( x - a ) n . If f ( x ) is periodic with period b , the Fourier series F ( x ) for f ( x ) is given by F ( x ) = a 0 + X n =1 ( a n cos(2 πnx/b ) + b n sin(2 πnx/b )) , where a 0 = 1 b Z b/ 2 - b/ 2 f ( x ) dx, a n = 2 b Z b/ 2 - b/ 2 f ( x ) cos(2 πnx/b ) dx, b n = 2 b Z b/ 2 - b/ 2 f ( x ) sin(2 πnx/b ) dx. The following Taylor series converge for all x : e x = X n =0 x n n ! , sin( x ) = X n =0 ( - 1) n x 2 n +1 (2 n + 1)! , cos( x ) = X n =0 ( - 1) n x 2 n (2 n )! . The following Taylor series converges for all
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Unformatted text preview: x with | x | < 1: (1 + x ) p = 1 + ∞ X n =1 p ( p-1) · · · ( p-n + 1) n ! x n . • Euler’s formula: e iθ = cos( θ ) + i sin( θ ). • The dot and cross products are: ~u · ~v = n X i =1 u i v i = || ~u |||| ~v || cos θ, ~u × ~v = det ~ i ~ j ~ k u 1 u 2 u 3 v 1 v 2 v 3 = || ~u |||| ~v || sin( θ ) ~n. 1...
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