Question

Using taylor series solve lim x→0 ((sin^-1 6x)-(sin 6x))/((tan^-1)(6x)-(tan 6x)

I don't know how to start this problem

Answer 1

you can use the techniques discussed here

http://math.stackexchange.com/questions/783469/evaluate-the-limit-with-taylor-series

to break it into pieces, and use the Taylor series to evaluate using the linearity of limits. Each function involved has a relatively easy-to-get series.