# What are the three conditions necessary for the function f(x) to be continuous at the point x = c?

Jun 23, 2016

#### Answer:

The necessary and sufficient conditions: $1. \lim h \to 0$ of f(c+h)) should exist. 2.$\lim h \to 0$ of $f \left(c - h\right)$ should exist. 3. f(c) should exist and $f \left(c\right) = f \left(c +\right) = f \left(c -\right)$.

#### Explanation:

The necessary and sufficient conditions: $1. \lim h \to 0$ of f(c+h))

should exist. 2.$\lim h \to 0$ of $f \left(c - h\right)$ should exist. 3. f(c) should

exist and $f \left(c\right) = f \left(c +\right) = f \left(c -\right)$.

If anyone of these is not satisfied, f(x) is discontinuous at x = c.

It is easy to see see continuity while making a hand-graph of y = f(x).

The graph can be drawn at x = c, without lifting the marker.

Note that, if any of $f \left(c\right) , f \left(c -\right) \mathmr{and} f \left(c +\right) = \pm \infty$,

the function does not exist, at x = c.

. .