Limits and Continuity

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What is a limit in calculus?

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A limit is a value that a function approaches as the input approaches a certain point.

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Define continuity in the context of functions.

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A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point.

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What does it mean for a function to be discontinuous?

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A function is discontinuous at a point if it is not continuous at that point, meaning the limit does not equal the function's value.

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The limit is 5.

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What is the Squeeze Theorem?

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What is a removable discontinuity?

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A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining it appropriately.

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What is the difference between one-sided limits and two-sided limits?

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A one-sided limit considers the value of the function as it approaches a point from one side (left or right), while a two-sided limit considers both sides.