Question

The function `tanx/|x|` ______

Options

• is continuous atx = 0

• is discontinuous at x = 0

• has removable discontinuity at x = 0

• none of these

Answer 1

The function `tanx/|x|` is discontinuous at x = 0.

Explanation:

`lim_{x→0^+} tanx/|x| = lim_{x→0}tanx/x = 1`

and `lim_{x→0^-}tanx/|x| = lim_{x→0}tanx/(-x) = -1`

∴ the given function is discontinuous at x = 0.