Paul's Online Notes
Home / Calculus II / Series & Sequences / Applications of Series
Show Mobile Notice Show All Notes Hide All Notes
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 views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 4-17 : Applications of Series

1. Determine a Taylor Series about $$x = 0$$ for the following integral. $\int{{\frac{{{{\bf{e}}^x} - 1}}{x}\,dx}}$ Solution
2. Write down $${T_2}\left( x \right)$$, $${T_3}\left( x \right)$$ and $${T_4}\left( x \right)$$ for the Taylor Series of $$f\left( x \right) = {{\bf{e}}^{ - 6x}}$$ about $$x = - 4$$. Graph all three of the Taylor polynomials and $$f\left( x \right)$$ on the same graph for the interval $$\left[ { - 8, - 2} \right]$$. Solution
3. Write down $${T_3}\left( x \right)$$, $${T_4}\left( x \right)$$ and $${T_5}\left( x \right)$$ for the Taylor Series of $$f\left( x \right) = \ln \left( {3 + 4x} \right)$$ about $$x = 0$$. Graph all three of the Taylor polynomials and $$f\left( x \right)$$ on the same graph for the interval $$\left[ {\displaystyle - \frac{1}{2},2} \right]$$. Solution