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9-1_Exploration

# 9-1_Exploration - 9.1 Exploration II Finding Power Series...

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Math 604 – AP Calculus BC Name_____________________________ 9.1 Exploration I: Finding Power Series for Other Functions Given that 1 / (1 ! x ) is represented by the power series 1 + x + x 2 + + x n + on the interval ( ! 1, 1) . 1. Find a power series that represents 1 / (1 + x ) on ( ! 1, 1) . 2. Find a power series that represents x / (1 + x ) on ( ! 1, 1) . 3. Find a power series that represents 1 / (1 ! 2 x ) on ( ! 1 2 , 1 2 ) . 4. Find a power series that represents 1 x = 1 1 + ( x ! 1) on (0, 2) . Could you have found the intervals of convergence yourself? 5. Find a power series that represents 1 3 x = 1 3 ! 1 1 + ( x " 1) # \$ % ( and give its interval of convergence.

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Unformatted text preview: 9.1 Exploration II: Finding Power Series by Differentiation and Integration 1. Given that 1 / (1 ! x ) is represented by the power series 1 + x + x 2 + … + x n + … on the interval ( ! 1, 1) , find a power series to represent 1 / (1 ! x ) 2 . Hint: notice that 1 / (1 ! x ) 2 is the derivative of 1 / (1 ! x ) . 2. Given that 1 1 + x = 1 ! x + x 2 ! x 3 + … + ( ! x ) n + … on the interval ( ! 1, 1) , find a power series to represent ln(1 + x ) . Hint: notice that 1 / (1 + x ) is the derivative of ln(1 + x ) ....
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9-1_Exploration - 9.1 Exploration II Finding Power Series...

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