Limits

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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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How do you find the limit as x approaches a specific value?

Back

To find the limit, substitute the value into the function if it is continuous at that point, or analyze the behavior of the function as it approaches that value.

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What does it mean if a limit is DNE (Does Not Exist)?

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A limit is DNE if the function does not approach a specific value as x approaches a certain point, often due to oscillation or unbounded behavior.

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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 x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

How do you determine vertical asymptotes?

Back

Vertical asymptotes can be found by setting the denominator of a rational function to zero and solving for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is continuity in a function?

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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 the limit as x approaches 3 from the left for the function f(x) = 4?

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The limit is 4.

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What is the limit as x approaches infinity for the function f(x) = 20?

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The limit is 20.

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What is the limit as x approaches 2 for the function f(x) = 1/(x-2)?

Back

The limit is DNE due to a vertical asymptote at x=2.

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What is the limit as x approaches 0 for the function f(x) = 1/x?

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The limit is DNE as it approaches infinity from the right and negative infinity from the left.