1.5 Infinite Limits and Limits at Infinity

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What is an infinite limit?

Back

An infinite limit occurs when the value of a function increases or decreases without bound as the input approaches a certain value.

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What does DNE stand for in limits?

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DNE stands for 'Does Not Exist', indicating that a limit cannot be determined.

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Evaluate the limit: @@ ext{lim}_{x ightarrow2}rac{x-6}{2-x}@@

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DNE

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Back

Front

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

Back

The limit of a polynomial function as x approaches infinity is determined by the leading term.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrowrac{3}{7}} rac{3x^2 + 2}{x - 1}@@

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Back

The limit is 0.

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What does it mean if a limit approaches infinity?

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If a limit approaches infinity, it means the function's values increase without bound as the input approaches a certain value.

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Evaluate the limit: @@ ext{lim}_{x ightarrow2^-} rac{x+8}{2-x}@@

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Front

What is the significance of limits at infinity?

Back

Limits at infinity help determine the behavior of functions as the input grows very large or very small.