Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
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.
- \( \displaystyle f\left( x \right) = \frac{6}{{1 + 7{x^4}}}\) Solution
- \( \displaystyle f\left( x \right) = \frac{{{x^3}}}{{3 - {x^2}}}\) Solution
- \( \displaystyle f\left( x \right) = \frac{{3{x^2}}}{{5 - 2\,\sqrt[3]{x}}}\) Solution
- Give a power series representation for the derivative of the following function. \[g\left( x \right) = \frac{{5x}}{{1 - 3{x^5}}}\] Solution
- Give a power series representation for the integral of the following function. \[h\left( x \right) = \frac{{{x^4}}}{{9 + {x^2}}}\] Solution