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Unformatted text preview: (problem 22) (1) Dierentiate the function f ( x ) = tan-1 (2 x ) (2) Represent the derivative of the function f ( x ) as a power series. (3) Note the function f ( x ) is the integral of the function in part 2. Use integration to Fnd a power series representation of the function f ( x ) and the radius of convergence. Section 11.9 Representations of Functions as Power Series 3 Example 2.2. (problem 14) (1) Find a power series representation for f ( x ) = ln(1 + x ) . What is the radius of convergence? (2) Use part (1) to nd a power series for f ( x ) = x ln(1 + x ) . (3) Use part (1) to nd a power series for f ( x ) = ln( x 2 + 1) ....
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