Determine the following limits. lim x→−∞ (2x-8 + 4x3)

Ch. 2 - Limits

Briggs - Calculus: Early Transcendentals 3rd Edition

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Briggs 3rd Edition

Ch. 2 - Limits

Problema 24

Capitolo 2, Problema 24

Determine the following limits.
lim x→−∞ (2x^-8+ 4x³)

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Identify the dominant term in the expression as \(x\) approaches \(-\infty\). The expression is \(2x^{-8} + 4x^3\).

Since \(x^3\) grows faster than \(x^{-8}\) as \(x\) approaches \(-\infty\), the term \(4x^3\) is dominant.

Rewrite the expression focusing on the dominant term: \(4x^3\).

Consider the behavior of \(4x^3\) as \(x\) approaches \(-\infty\).

Conclude that the limit of the expression is determined by the behavior of the dominant term \(4x^3\) as \(x\) approaches \(-\infty\).

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