Definition of Continuity:1) ___________________2) ___________________3) ___________________
1) f(c) is defined2) lim x->c of f(c) exits3) lim x-> c of f(x) = f(c)
1) Continuity is a property of a function where it has no abrupt changes or gaps in its graph, meaning the function has a smooth and uninterrupted flow.
2) More precisely, a function f(x) is continuous at a point x=a if f(a) exists, and the limit of f(x) as x approaches a exists and is equal to f(a).
3) Continuity can also be defined in terms of intervals, where a function is continuous on an interval if it is continuous at every point in that interval. A function is said to be continuous on a closed interval if it is continuous at every point within that interval and also at the endpoints of the interval.
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