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

1 Answer
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(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.

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