Understanding the Three Conditions for Continuity in Mathematics

f is continuous at x=c if…

f is continuous at x=c if three conditions are satisfied:

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f is continuous at x=c if three conditions are satisfied:

1. f(c) is defined: The function must have a defined value at x=c. In other words, the function should be defined at the point c.

2. The limit of f(x) as x approaches c exists: The limit of the function f(x) as x approaches c must exist. This means that the function approaches a specific value as x gets arbitrarily close to c from both sides.

3. The limit of f(x) as x approaches c is equal to f(c): Finally, the limit of f(x) as x approaches c should be equal to the value of f(c). In other words, the value of the function at x=c should be the same as the limit of the function at that point.

These three conditions ensure that the function is continuous at x=c, meaning that it has no jumps, holes, or any other disruptions in its graph at that specific point.

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