Limits to Infinity HW #1

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Define the limit of a function as x approaches infinity.

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The limit of a function as x approaches infinity describes the behavior of the function as the input values grow larger and larger. It indicates the value that the function approaches as x increases without bound.

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2

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-6

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-2

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0

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Explain the concept of Dominant Terms in limits to infinity.

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In limits to infinity, the dominant term is the term with the highest degree in the numerator or denominator. As x approaches infinity, the behavior of the function is primarily determined by these dominant terms.

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What happens to the limit of a rational function if the degree of the numerator is less than the degree of the denominator?

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If the degree of the numerator is less than the degree of the denominator, the limit as x approaches infinity is 0.

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What happens to the limit of a rational function if the degree of the numerator is greater than the degree of the denominator?

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If the degree of the numerator is greater than the degree of the denominator, the limit as x approaches infinity is either +∞ or -∞, depending on the leading coefficients.

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1

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