Continuity at a point means that both the limit and value of the function exist and are equal at that specific point.
Imagine walking along an unbroken path without any gaps or jumps. You can smoothly transition from one step to another without any interruptions.
Continuous Function: A function for which every small change in input results in only a small change in output, without any sudden jumps or breaks.
Discontinuous Function: A function that has one or more points where it is not continuous.
Intermediate Value Theorem: A theorem that states if a function is continuous on a closed interval, then it takes on every value between the values of the endpoints.
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