Let x = 0 + h, when x is tends to 0⁺

Since x tends to 0, h will also tend to 0.

Right Hand Limit(R.H.L.):

=

= sin ∞

= ∞

Let x = 0 - h, when x is tends to 0^-

Since x tends to 0, h will also tend to 0.

Left Hand Limit(L.H.L.):

=

=

= - sin ∞

= -∞

Since,

∴ does not exist.