Calculus Special Trig Limits

Question

I'm stuck on this problem: Lim x approaching 0 (Sec(x) - 1) / (sin(x)

Answer 1

lim_x→0 [(secx - 1) / sinx]

Direct substitution yields the indeterminate form 0/0.

Applying L'Hopital's Rule, the given limit is equivalent to:

lim_x→0 [(secxtanx) / cosx)] = lim_x→0 [sinx / cos³x] = lim_x→0 [(1 / cos³x)(sinx)] = (1)(0) = 0

Answer 2

Consider only the limit of the numerator.