The limits can be done using multiple LHopitals Rule steps. Power series provide an alternative approach. In

Question:

The limits can be done using multiple L’Hôpital’s Rule steps. Power series provide an alternative approach. In each case substitute in the Maclaurin series for the trig function or the inverse trig function involved, simplify, and compute the limit.

lim x0 sin x - x + x5 6