Limx →-∞ (1)/(x)=0

Name: Problem 67, Chapter 2: Calculus Early Transcendentals
Uploaded: 2021-08-11T20:35:23-08:00
Duration: 1 min 5 s
Channel: Carson Merrill
Description: limx →-∞ (1)/(x)=0

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Key Concepts

Reciprocal Function Behavior

The reciprocal function, represented by 1/x, is a simple rational function that inversely relates its output to its input. Analyzing this function as x tends to infinity (or negative infinity) helps illustrate concepts of diminishing returns and asymptotic approach toward a horizontal line, typically the x-axis.

Asymptotic Behavior

Asymptotic behavior refers to the tendency of a function to approach a particular value as the input variable gets increasingly large in magnitude. In this context, it explains why the graph of 1/x gets arbitrarily close to the horizontal axis (y=0) as x approaches negative infinity, despite never actually reaching it.

Limits at Infinity

Limits at infinity deal with the behavior of a function as the variable grows without bound, either positively or negatively. This concept helps in understanding how functions behave in the long run, characterizing end behavior by describing the trend of outputs as the input becomes arbitrarily large or small.

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