Series Free Response Questions

# Series Free Response Questions - Ms Waldron BC Calculus...

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Ms. Waldron BC Calculus Serious Series Free Response Questions 1987 - BC 4 a) Find the first five terms in the Taylor series about x = 0 for 1 f(x) = 1 - 2x . b) Find the interval of convergence for the series in part (a). c) Use partial fractions and the result from part (a) to find the first five terms in the Taylor series about x = 0 for ( )( ) 1 g(x) = 1 - 2x 1 x - 1988 – BC 4 Determine all values of x for which the series ( ) k k k 0 2 x ln k 2 = + converges. Justify your answer. 1990 – BC 5 Let f be the function defined by 1 f(x) = x 1 - . (a) Write the first four terms and the general term of the Taylor series expansion of f(x) about x = 2. (b) Use the result from part (a) to find the fist four terms and the general term of the series expansion about x = 2 for ln | x – 1 |. (c) Use the series in part (b) to compute a number that differs from 3 ln 2       by less than 0.05. Justify your answer.

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1991 – BC 5 Let f be the function given by ( ) 2 4 f t = 1 + t and G be the function given by ( ) ( ) x 0 G x = f t dt . (a) Find the first four nonzero terms and the general term for the power series
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