lim_{x - 4} sin(x - 4) / (x - 4) = ___________

Question

lim_{x -> 4} sin(x - 4) / (x - 4) = ___________

Accepted Answer

1 This is the classic standard limit lim_{t->0} sin(t)/t = 1, applied with the substitution t = x - 4. As x -> 4, t -> 0, so the limit equals 1. It does not require L'Hopital or Taylor series; recognition of the standard form is all that is needed.