In Exercises 37-54, find the limit (if it exists). limx →0^-(x^2-(1)/(x))

Name: Problem 48, Chapter 1: Calculus of a Single Variable
Uploaded: 2020-11-03T04:16:16-08:00
Duration: 2 min 33 s
Channel: Samuel Goyette
Description: In Exercises 37-54, find the limit (if it exists). limx →0^-(x^2-(1)/(x))

step 1 Okay, so we have once again a limit of x squared minus 1 over x when x goes to 0 from the negati

In Exercises 37-54, find the limit (if it exists). limx...

Key Concepts

Dominant Term Analysis

Dominant term analysis involves identifying the term in an expression that has the greatest effect on the behavior of the function as the variable approaches a particular point. In limits, especially those involving sums of terms, the term that grows fastest (or decreases most rapidly) determines the behavior of the overall function, allowing simplification of the limit evaluation.

Infinite Limit

An infinite limit refers to a situation where the values of a function grow without bound (either positively or negatively) as the input approaches a certain value. This indicates that the function does not approach any finite value; instead, it diverges, often signifying the presence of a vertical asymptote or unbounded growth.

One-sided Limit

A one-sided limit specifically examines the behavior of a function as the input approaches a certain value from one side only – either from the left (values less than the point) or from the right (values greater than the point). This concept is critical when the function exhibits different behaviors on either side of a point, such as in cases of discontinuity or directional asymptotes.

Limit

The limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a particular value. It forms the basis for defining continuity, derivatives, and integrals by focusing on what value the function seems to approach, even if the function does not actually reach that value at the point.

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