Question

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

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

Calculus an Applied Approach

Calculus an Applied Approach

Ron Larson, David C,… 8th Edition

Chapter 3, Problem 38

Instant Answer

Solved by Expert Dwijendra Rao

06/13/2021

Step 1

We can rewrite this expression as $2-\frac{1}{x^3}$. Show more…

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

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Key Concepts

Limits at Infinity

This concept involves evaluating the behavior of functions as the variable approaches infinity. It helps in identifying which terms in the function dominate and which terms become negligible, ultimately determining the function's trend or value at large inputs.

Negative Exponents and Power Functions

Negative exponents indicate reciprocals of positive powers, so expressions like x?³ are equivalent to 1/x³. In the context of limits, as x approaches infinity, terms with negative exponents tend toward zero because the denominator grows without bound.

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