f(x) = (2^3x - 1)/tan x, x < 0

Question

Discuss the continuity of the following functions.

\(f(x)=\frac{2^{3x}-1}{tan\,x},\) x < 0

f(x) = (2^3x - 1)/tan x, x < 0

\(=\frac{x^2}{e^x + e^{-x}-2},\) x > 0

= 2, x = 0 at x = 0.

Answer 1

f(x) = (2^3x - 1)/tan x

∴ f(0) does not exist

∴ f is discontinuous at x = 0