Calculus Intro Review

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What is continuity in a function?

Back

A function is continuous at a point if the following three conditions are met: 1) The function is defined at that point, 2) The limit of the function as it approaches that point exists, 3) The limit equals the function's value at that point.

Tags

CCSS.HSF-IF.C.7D

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What does it mean if a limit does not exist at a point?

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A limit does not exist at a point if the function approaches different values from the left and right sides, or if it approaches infinity.

Tags

CCSS.HSF.IF.A.2

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What is the definition of a limit?

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The limit of a function at a point is the value that the function approaches as the input approaches that point.

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How do you determine if a function is continuous at a specific point?

Back

To determine continuity at a point, check if the function is defined at that point, if the limit exists, and if the limit equals the function's value.

Tags

CCSS.HSF-IF.C.7D

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What is the difference between a removable and a non-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. A non-removable discontinuity cannot be fixed by redefining the function at that point.

Tags

CCSS.HSF-IF.C.7D

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What is the Intermediate Value Theorem?

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The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], then it takes every value between f(a) and f(b) at least once.

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What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a.

Tags

CCSS.HSF-IF.C.7D

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What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that a function approaches as the input approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

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What is the Squeeze Theorem?

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The Squeeze Theorem states that if f(x) ≤ g(x) ≤ h(x) for all x in some interval, and if the limits of f(x) and h(x) both equal L as x approaches a, then the limit of g(x) as x approaches a also equals L.

Front

What is the definition of a derivative?

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The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.