Question

Find the limit lim 5tan^-1 (ln3x) x>infinity

Answer 1

Lim ln(3x)=∞  as x->∞
tan^(-1)(∞)=π(k+1/2)   where k is an integer.
Therefore
lim 5tan^(-1)(ln(3x))=5(k+1/2)π as x-> ∞  and where k∈Z (i.e. integers)