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

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Answer 1 · 2014-10-19T14:27:29

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.