I am teaching a Calculus class and we are finishing up power/Taylor series this week. The last section of the chapter is on applications, but the only ones listed there are approximating non-rational numbers like $\sqrt{1.02}$ and computing limits like $\lim_{x\to 0}\frac{\sin x}{x}$. I would like to find better examples that may or may not have a quick physical application (I cannot assume they know any physics beyond what I can explain). So, my question is, do any of you know some applications of Taylor series that I could spend maybe about half an hour to forty five minutes doing? They needn't be physical applications, just interesting. I have already done Euler's formula. Also, we do not deal with any remainder theorems in this class. Thanks.
Calculus – The Power of Taylor Series Explained
calculuseducationpower series
Best Answer
Not quite on the power of Taylor's series, but you could use the Taylor series for $f(x) = e^x$ to show that $e$ is irrational.