I am presently struggling in finishing this problem:
Determine the Taylor series representation of the function $f(x)=e^{3x}$. Then, determine the approximate value of $e^{1.2}$ using the series with a relative approximate error of less than 0.1%.
Finding the Taylor series representation is easy. It is equal to $\sum_{n=0}^{\infty } \frac{3x^{n}}{n!}$.
What should I do with the second part of the problem? If the formula $f(x)=T_{n}(x)+R_{n}(x)$ is not applicable for this case, then I couldn't find a formula elsewhere that relates the formula for relative error and the approximate value. I suspect that Taylor Polynomial should be applied. If it is to be applied, then how can I obtain the degree based on the relative approximate error?
What I actually thought is to use the relative error formula directly since I already know the values for the relative error (0.001) and the true value ($e^{1.2}$). However, I know that that is the wrong approach because there are given values in the problem.
Any help would be appreciated. Thanks.