Unit 1 Review

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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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It means that as x approaches a, the function f(x) approaches the value L.

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What is the limit of a polynomial function as x approaches a number?

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The limit of a polynomial function as x approaches a number is simply the value of the polynomial at that number.

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5

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What does it mean for a function to be continuous at a point?

Back

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 the significance of the Intermediate Value Theorem?

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The Intermediate Value Theorem states that if a function is continuous on an interval, it takes on every value between its values at the endpoints of the interval.

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0

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What is the definition of a continuous function?

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A function is continuous if it is defined at a point, the limit exists at that point, and the limit equals the function's value.

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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.