6.3: Infinite Limits

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Define Infinite Limits in calculus.

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Infinite limits refer to the behavior of a function as the input approaches a certain value, resulting in the function's output increasing or decreasing without bound (approaching infinity or negative infinity).

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-5.

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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 does not approach a finite value.

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Explain how to determine the limit of a rational function as x approaches infinity.

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To determine the limit of a rational function as x approaches infinity, compare the degrees of the numerator and denominator. If the degree of the numerator is greater, the limit is infinity; if less, the limit is zero; if equal, divide the leading coefficients.

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What is the significance of the leading term in polynomial limits?

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The leading term of a polynomial dominates the behavior of the function as x approaches infinity or negative infinity, determining the limit.

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Define the term 'asymptote' in relation to limits.

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An asymptote is a line that a graph approaches but never touches, often indicating the behavior of a function as it approaches infinity.