Question

Lim
θ→0 (cos 9θ − 1)/(sin 8θ)

Answer 1

`\lim_(t \to 0) (cos 9 t - 1)/(sin 8 t) = (1-1)/(0)= (0)/(0)`
We can use the L`Hospitals rule:

`\lim_(t \to 0) (cos 9 t - 1)/(sin 8 t)= \\ =\lim_(t \to 0) (-9 * sin 9 t)/(8 * cos 8 t)= (0)/(8)= 0`

Answer 2

lim as θ → 0 of (cos 9θ - 1)/sin 8θ = lim as θ → 0 of (-9sin 9θ) / 8cos 8θ = 0/8 = 0