L26 Representation of Functions as Power Series II

L26 Representation of Functions as Power Series II - 2 x 4...

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Lecture 26: Representation of functions as Power Series(II) Use the power series 1 X n =0 x n = 1 1 ± x ; j x j < 1 to ±nd power series representations of the following functions: ex. f ( x ) = 1 (1 ± x ) 2 1

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ex. f ( x ) = x (1 ± 2 x ) 2 2
ex. Evaluate the inde±nite integral as a power series. What is the radius and interval of convergence? Z ln(1 ± t ) t dt 3

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NYTI: Find the power series representation of the following functions: 1. 4 x + 2
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Unformatted text preview: ; 2. x 4 + 9 x 2 3. x (1 ± x ) 3 4. (a)Evaluate f ( x ) = Z 1 1 + x 5 dx as a power series. (b) Use the integral to approximate Z : 2 1 1 + x 5 dx correct to 3 decimal places. 5. Find a power series representations for (a) arctan(2 x ) (b) ln(5 ± x ) Tonight’s Homework: Write functions as power series. 4...
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L26 Representation of Functions as Power Series II - 2 x 4...

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