In Exercises 37-54, find the limit (if it exists). limx →-3^- (x+3)/(x^2+x-6)

Name: Problem 43, Chapter 1: Calculus of a Single Variable
Uploaded: 2020-11-03T04:06:56-08:00
Duration: 4 min
Channel: Samuel Goyette
Description: In Exercises 37-54, find the limit (if it exists). limx →-3^- (x+3)/(x^2+x-6)

step 1 Okay, so we have this equation here and we want to know what's happening with the limit of x plu

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

Key Concepts

Limits

Limits are a fundamental concept in calculus that describe the behavior of functions as the input approaches a particular value. They are used to analyze the behavior of functions near points where they may not be explicitly defined, thereby laying the groundwork for the study of continuity, derivatives, and integrals.

One-sided Limits

One-sided limits focus on the behavior of a function as the variable approaches a specific value from one side only, either from the left or the right. This is particularly important when the function behaves differently on either side of the point or when considering functions with discontinuities.

Algebraic Manipulation and Factoring

Algebraic manipulation, especially the technique of factoring polynomials, is crucial in the process of limit evaluation. Factoring allows for the cancellation of common factors in the numerator and denominator, eliminating indeterminate forms and simplifying the evaluation of the limit at points where the original function may not be directly defined.

Rational Functions

Rational functions are expressions formed by dividing one polynomial by another. Evaluating limits involving rational functions often involves simplifying the expression through factoring, which can help identify removable discontinuities or vertical asymptotes, thereby clarifying the function's behavior near points of interest.

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