How accurate is solving limits using Taylor series expansion really is?

I have been doing limits and in many questions (involving trigonometric or logarithmic or exponential terms) the solution tell me to expand the terms using Taylor series until the degree of numerator and denominator matches and then solve the question. But how accurate is this method? I mean we do get the correct answer using this method but I am not sure how accurate or correct method it is, maybe only for the questions at my level (as the questions are made so that we get we get the answer after only expanding one ot two temrs) please explain.

Thanks in advance!