Question

How do you do this question?

Answer 1

Explanation:

arctan(x) is less than π/2 for x > 0. Therefore, if we say g(x) = 13 (π/2) / eˣ, then f(x) < g(x) for all values of x > 0.

g(x) = 13 (π/2) / eˣ

g(x) = 13π/2 · (1/e)ˣ

So g(x) is a geometric series where r = 1/e. Since |r| < 1, the series converges.

Since g(x) converges, the smaller f(x) also converges.