Question

Find the limits. $$ \lim _{x \rightarrow+\infty}\left(1+2 x-3 x^{5}\right) $$

   Find the limits.
$$
\lim _{x \rightarrow+\infty}\left(1+2 x-3 x^{5}\right)
$$

Calculus Early Transcendentals

Calculus Early Transcendentals

Howard Anton, Irl… 9th Edition

Chapter 1, Problem 9

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Solved by Expert Amy Jiang

08/14/2020

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In this case, it is $x^5$. Show more…

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Find the limits. $$ \lim _{x \rightarrow+\infty}\left(1+2 x-3 x^{5}\right) $$

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Key Concepts

Dominant Term in Polynomials

When evaluating limits of polynomial functions as the variable tends to infinity, the term with the highest power has the most significant impact on the function's behavior. Lower degree terms become negligible compared to the dominant term, which allows for a simplified analysis of the function's end behavior.

Limits at Infinity

This concept involves finding the behavior of a function as the independent variable approaches infinity (or negative infinity). In many cases, especially with polynomials, the highest degree term dominates the value of the function as the variable grows very large, which determines the limit.

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