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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