Using a geometric construction and the squeeze theorem, find lim θ→0^+ tanθ /θ

Question

lim tanθ/θ

θ→0^+

Answer 1

We just replace tag (X) with Sin (X) / Cos (X) and knowing that lim as X->0 sin (X) / X = 1 , so:

Lim as X -> 0 tan (X) / X = lim as X -> 0 sin (X) / Cos (X) . 1 / X = lim as X -> 0 sin (X ) / X . 1 / Cos (X) =

lim as X -> 0 sin (X) / X . lim as X -> 0 1 / cos (X) = 1 . 1/1 = 1