If a function is continuous at a point,

1. the limit of the function may not exist at the point.
2. the function must be derivable at the point.
3. the limit of the function at the point tends to infinity.
4. the limit must exist at the point and the value of limit should be same as the value of the function at that point.

We k now t hat f(x) i s cont i nuous at x = a, if lim (x → a) f(x) exists and equal to f (a).