Understanding Continuity in Mathematics | Explaining the Conditions for a Function to be Continuous at x = a

Continuous at x = a

A function f(x) is said to be continuous at x = a if three conditions are satisfied:

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A function f(x) is said to be continuous at x = a if three conditions are satisfied:

1. f(a) is defined: The value of the function at x = a should be well-defined and not have any ambiguities or restrictions.

2. The limit of f(x) as x approaches a exists: The limit of f(x) as x approaches a from both the left and the right sides should exist and be finite. In other words, the left-hand limit and the right-hand limit at x = a should be equal.

3. The limit of f(x) as x approaches a is equal to f(a): The value of the function at x = a should be equal to the limit of the function as x approaches a.

If these conditions are met, then the function is said to be continuous at x = a. This means that there are no sudden jumps, holes, or disruptions in the graph of the function at x = a. The function can be drawn without lifting the pencil from the paper at x = a.

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