Question

How do I use a power series to calculate a limit?

Answer 1

Here is a simple application of a power series in evaluating a limit.

`lim_{x to 0}{sinx]/x`

by replacing `sinx` by its Maclaurin series.

`=lim_{x to 0}{x-x^3/{3!}+x^5/{5!}-x^7/{7!}+cdots}/{x}`

by distributing the division to each term,

`=lim_{x to 0}(1-x^2/{3!}+x^4/{5!}-x^6/{7!}+cdots)`

by sending `x` to zero,

`=1-0+0-0+cdots`

since all but the first term are zero,

`=1`

---

I hope that this was helpful.