Question

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

Answer 1

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

Explanation:

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

should exist. 2.`lim h to 0` of `f(c-h)` should exist. 3. f(c) should

exist and `f(c)=f(c+)=f(c-)`.

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(c), f(c-) and f(c+)=+-oo`,

the function does not exist, at x = c.

. .