A continuous function is one that has no breaks, holes, or jumps in its graph. It can be drawn without lifting the pen from the paper.
Discontinuous Function: A discontinuous function has one or more breaks, holes, or jumps in its graph. It cannot be drawn without lifting the pen from the paper.
Intermediate Value Theorem: This theorem states that if a continuous function takes on two different values at two points within an interval, then it must also take on every value between those two points within that interval.
Limit: The limit of a function represents what value it approaches as the input gets arbitrarily close to a certain point. It helps determine behavior near points of discontinuity and infinity.
AP Calculus AB/BC - 2.4 Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
If f(x) is a continuous function defined over the interval [a,b], what does the integral \int_{a}^{b} f(x) ,dx represent?
For a continuous function f(x) over an interval [a, b], which of the following statements is true about the average value of f(x)?
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