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

Name: Problem 40, Chapter 1: Calculus of a Single Variable
Uploaded: 2020-11-03T03:49:47-08:00
Duration: 2 min 31 s
Channel: Samuel Goyette
Description: In Exercises 37-54, find the limit (if it exists). limx →1^+ (2+x)/(1-x)

step 1 Once again, we look at a limit. So we want to know what's the behavior of this function of this

In Exercises 37-54, find the limit (if it exists). limx →1^+...

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Key Concepts

Asymptotic Behavior and Infinite Limits

When a function’s denominator approaches zero while its numerator remains nonzero, the values of the function can increase or decrease without bound, leading to infinite or negative infinite limits. The sign of the function as you approach the limit point determines whether it tends to positive or negative infinity.

One-Sided Limits

A one-sided limit considers the behavior of a function as the input approaches a specific value strictly from one side (either from the left or the right). This is crucial when the function behaves differently when approached from different directions, such as near discontinuities.

Behavior of Rational Functions Near Discontinuities

Rational functions, which are ratios of polynomials, can exhibit discontinuities when the denominator equals zero. Analyzing the limit near such points involves understanding how the numerator and denominator behave relative to each other as the variable approaches the critical value.

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