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 some value.

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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 undefined because the denominator becomes zero.

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The limit is -1.

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The limit is 3.

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What is the definition of a one-sided limit?

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A one-sided limit is the value that a function approaches as the input approaches a specific point from one side (left or right).

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What is the Squeeze Theorem?

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The Squeeze Theorem states that if a function is squeezed between two other functions that have the same limit at a point, then the squeezed function also has that limit at that point.

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What is the difference between removable and non-removable discontinuities?

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Removable discontinuities can be 'fixed' by redefining the function at that point, while non-removable discontinuities cannot.

Tags

CCSS.HSF-IF.C.7D

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