Question

$\lim_{x\to\infty} tan^{-1}x$

Answer 1

$\frac{\pi}{2}$

Answer 2

The limit $\lim_{x\to\infty} \tan^{-1}x$ represents the value the inverse tangent function approaches as its argument $x$ tends to infinity. The range of $\tan^{-1}x$ is $(-\frac{\pi}{2}, \frac{\pi}{2})$. As $x$ increases without bound, $\tan^{-1}x$ approaches the upper limit of its range, which is $\frac{\pi}{2}$. This is because $\tan y \to \infty$ as $y \to \frac{\pi}{2}^-$.