Evaluating Limits by Factoring

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What is the definition of 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 if a limit is said to be 'DNE'?

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DNE stands for 'Does Not Exist', indicating that the limit does not approach a finite value.

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How do you evaluate limits by factoring?

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To evaluate limits by factoring, factor the expression, cancel common terms, and then substitute the limit value.

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The limit is 2, after factoring and canceling the common term.

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What is the significance of the limit approaching a finite number?

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It indicates that the function behaves predictably as it approaches that point.

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What happens to the limit if the numerator and denominator both approach zero?

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This is an indeterminate form, and further analysis (like L'Hôpital's Rule) is needed.

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What is L'Hôpital's Rule?

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The limit is 1.

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What is the limit of a constant function?

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