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PhysicsHelp12
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thanks I think I got it :)
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A continuous function is a mathematical function that does not have any sudden jumps or breaks in its graph. This means that the function is defined and can be evaluated at every point along its domain.
A function is continuous if it satisfies three conditions: 1) the function is defined at the point in question, 2) the limit of the function at that point exists, and 3) the value of the function at that point is equal to the limit. If all three conditions are met, the function is considered continuous at that point.
A continuous function is one that is defined and can be evaluated at every point in its domain, while a discontinuous function is one that has breaks or jumps in its graph. This means that a discontinuous function is not defined at certain points in its domain.
Continuous functions are used in many areas of science, engineering, and economics to model real-life phenomena. For example, they can be used to describe the growth of a population, the spread of a disease, or the behavior of a stock market. They are also essential in calculus, as they allow us to analyze and solve problems involving rates of change and optimization.
Yes, it is possible for a function to be continuous at one point but not at others. This happens when the function satisfies the three conditions for continuity at one point, but fails to satisfy one or more of these conditions at other points in its domain. In this case, the function is considered to be discontinuous at those points.