Question

find the limit of lim cos (2tan^(-1)x)) as x->+infinity

Answer 1

We can find the limit as x approaches positive infinity by finding the limit inside the cosine first. The limit as x -> infinity of 2arctanx is 2*pi/2 because there is a horizontal asymptote for arctanx at x = pi/2. So, we then evaluate cos(2pi/2) = cos(pi) = -1.