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 can indicate a specific value, infinity, or that the limit does not exist (DNE).

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What does it mean if the limit of a function is infinity?

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If the limit of a function is infinity, it means that as x approaches a certain value (or infinity), the function's output grows without bound.

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

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The limit of a constant function as x approaches infinity is the constant value itself.

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Explain the concept of 'Dominant Term' in limits to infinity.

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The dominant term is the term in a polynomial that grows the fastest as x approaches infinity. It determines the limit of the function.

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How do you find the limit of a rational function as x approaches infinity?

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To find the limit of a rational function as x approaches infinity, divide all terms by the highest power of x in the denominator.