Select the best answer below:

Question

lim x→∞ [ln(|x|-1)] / (cos(x))^x

a) does not exist
b) 1
c) -1
d) 0

Thank you very much for your helppppp in advance

Answer 1

clearly, lim x→∞ ln(|x|-1) = ∞
(cos(x))^x oscillates between 0^∞ and 1^∞
That means the limit oscillates between ∞/0 and ∞/1
In either case, it is undefined.