the function is continuous at x=a if
A function is said to be continuous at a particular point, x=a, if the following conditions are met:
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A function is said to be continuous at a particular point, x=a, if the following conditions are met:
1. The function must be defined at x=a. In other words, there should be a meaningful value for the function at x=a.
2. The limit of the function as x approaches a must exist. This means that as x gets closer and closer to a, the function values should approach a specific value.
3. The limit value of the function as x approaches a must be the same as the actual value of the function at x=a. This ensures that there are no abrupt changes or discontinuities at x=a.
In simpler terms, a function is continuous at x=a if there are no holes, jumps, or gaps in the graph of the function at that point. The function should provide a smooth and connected curve around x=a without any sudden changes.
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