Question

Given a value for epsilon > 0, find an expression for N which will guarantee that |arctan(n) - L| < epsilon whenever n>NGiven a value for epsilon > 0, find an expression for N which will guarantee that |arctan(n) - L| < epsilon whenever n>N@Mathematics

Answer 1

When I get to step
arctan(n) < epsilon + L
can you say:
tan(epsilon + L) < n ??

Answer 2

Not quite. The point is of course that L = pi/2 and the limit of arctan x as x --> infinity is L. tan itself is discontinuous at pi/2 therefore tan(pi/2 + epsilon) is for small epsilon large and negative.

Anyway, knowing now what L is, do you have another idea?