\(\lim\limits_{\text x \to0}sin\cfrac1{\text x}
\)
lim(x→0) sin 1/x
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.):
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.):
\(\therefore \lim\limits_{\text x \to0}sin\cfrac1{\text x}
\) does not exist.