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Section 10.15 : Power Series and Functions

For problems 1 – 3 write the given function as a power series and give the interval of convergence.

1. \( \displaystyle f\left( x \right) = \frac{6}{{1 + 7{x^4}}}\) Solution
2. \( \displaystyle f\left( x \right) = \frac{{{x^3}}}{{3 - {x^2}}}\) Solution
3. \( \displaystyle f\left( x \right) = \frac{{3{x^2}}}{{5 - 2\,\sqrt[3]{x}}}\) Solution
4. Give a power series representation for the derivative of the following function. \[g\left( x \right) = \frac{{5x}}{{1 - 3{x^5}}}\] Solution
5. Give a power series representation for the integral of the following function. \[h\left( x \right) = \frac{{{x^4}}}{{9 + {x^2}}}\] Solution