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Relation between Continuity and Differentiability

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Question

What is the meaning of ,"Function is not continuous at a point" ?

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Solution

In a function f(x), if f(x) increases (or decreases) by an incremental value when x is increased (or decreased) respectively by an incremental value, then f(x) is said to be continuous. In other words, f(x) is continuous when the graph of f(x) is a single unbroken curve, and throughout the curve there are no abrupt "holes" or "jumps".
So if these broken, holes or jumps are there then function is not continuous at that point.

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