Question

Find $\lim _{x \rightarrow 0^{-}}\left(\frac{1}{x}+\frac{1}{x^{2}}\right).$

   Find $\lim _{x \rightarrow 0^{-}}\left(\frac{1}{x}+\frac{1}{x^{2}}\right).$

Calculus A New Horizon

Calculus A New Horizon

Howard Anton 6th Edition

Chapter 2, Problem 54

Instant Answer

Solved by Expert Carson Merrill

07/02/2021

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Step 1: We are given the function $\frac{1}{x}+\frac{1}{x^{2}}$ and we are asked to find the limit as $x$ approaches $0$ from the left. Show more…

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Find $\lim _{x \rightarrow 0^{-}}\left(\frac{1}{x}+\frac{1}{x^{2}}\right).$

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Key Concepts

Dominant Terms

In expressions involving sums, identifying the dominant term—that is, the term which grows most rapidly as the variable approaches a certain value—is essential. This helps in simplifying the evaluation of limits by focusing on the term that dictates the overall behavior of the function.

Asymptotic Behavior

Asymptotic behavior examines how a function behaves as its variable approaches a particular value, often where the function becomes unbounded (approaches infinity or negative infinity). Recognizing such behavior is key in understanding limits at points where the function is not finite.

One-Sided Limit

A one-sided limit considers the behavior of a function as the variable approaches a point from only one side (either from the left, denoted as x ? c?, or from the right, denoted as x ? c?). This is crucial when the behavior of the function is different on each side of that point.

Limit

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a particular value. It enables the determination of the value that a function approaches, even if the function is not defined at that exact point.

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