Definition of Continuity:1) ___________________2) ___________________3) ___________________
Definition of Continuity:
1) In general, a function f(x) is said to be continuous at a point x = a if the following three conditions are satisfied:
a) The function is defined at x = a
Definition of Continuity:
1) In general, a function f(x) is said to be continuous at a point x = a if the following three conditions are satisfied:
a) The function is defined at x = a.
b) The limit of the function as x approaches a exists.
c) The limit of the function as x approaches a is equal to the value of the function at x = a.
In simple terms, it means that there are no breaks, jumps, or holes in the graph of the function at x = a.
2) A function f(x) is said to be continuous on an interval if it is continuous at every point within that interval. This implies that there are no jumps, breaks, or holes in the graph of the function within the specified interval.
3) We say a function f(x) is continuous on its domain if it is continuous at every point within its domain. The domain of the function is the set of values for which the function is defined.
Overall, continuity describes the smoothness and unbroken nature of a function, implying that there are no sudden changes or abrupt transitions in its behavior.
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