Limits REVIEW

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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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What does it mean for a limit to exist?

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A limit exists if the function approaches the same value from both the left and right sides as the input approaches a certain point.

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What is the limit of a constant function?

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The limit of a constant function as x approaches any value is the constant itself.

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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 continuity at a point?

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

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What is 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 infinite discontinuity?

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Infinite discontinuity occurs when the function approaches infinity as the input approaches a certain value.

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What is jump discontinuity?

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Jump discontinuity occurs when the left-hand limit and right-hand limit at a point exist but are not equal.

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How do you evaluate limits using substitution?

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To evaluate limits using substitution, simply substitute the value of x into the function, provided the function is defined at that point.

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