# Trigonometric Limit!

Calculus Level 2

Evaluate

$\displaystyle \lim_{x \to 999^+} \tan^{-1} \left(\frac{1}{x - 999}\right).$

Details and assumptions

$$\tan^{-1}x$$ denotes the inverse of $$\tan x$$ and not the reciprocal $$\frac{1}{\tan x}$$.

The principal branch of $$\tan^{-1}$$ is $$\left( -\frac{\pi}{2}, \frac{\pi}{2}\right)$$.

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