Trigonometric Limit!

Calculus Level 2

Evaluate

limx999+tan1(1x999). \displaystyle \lim_{x \to 999^+} \tan^{-1} \left(\frac{1}{x - 999}\right).

Details and assumptions

tan1x\tan^{-1}x denotes the inverse of tanx\tan x and not the reciprocal 1tanx\frac{1}{\tan x}.

The principal branch of tan1 \tan^{-1} is (π2,π2)\left( -\frac{\pi}{2}, \frac{\pi}{2}\right).

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