# Error Bound on Tangent Maclaurin Series

Salutations! Just checking if my logic is correct.

## Homework Statement

I need to bound the error for $$\tan x$$ on $$[0, \frac{\pi}{2}]$$

## Homework Equations

$$R_n(x) = \displaystyle \frac{\tan^{n+1}(\zeta)}{(n+1)!}x^{n+1}$$

## The Attempt at a Solution

So...I thought that the error should go to 0 since the factorial will eventually overtake the polynomial. Then, I thought that this logic might break down since $$\tan x$$ goes to infinity on the interval. Am I overthinking this?

Thanks!