What is continuity at a point?


Continuity at a aim instrument that you can inhale the office at that aim externally lifting up your pencil. Or in past technical conditions, a insignificant fluctuate in x produces merely a insignificant fluctuate in f(x)

In prescribe for a office to be consecutive at a aim it must prosper three criteria: 1) f(A) must be defined 2) f(x) has a boundary as x approaches A from twain direction 3) the boundary as x approaches A is in-effect resembling to f(A)

To visualize this, under is a consecutive graph at aim A. Notice how you could inhale this externally cream up your pencil.

Now under is a graph that is disconsecutive for multiple reasons. Notice how you would feel to pluck up your pencil to inhale this graph.

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