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

Name: Problem 38, Chapter 1: Calculus of a Single Variable
Uploaded: 2020-11-17T04:31:03-08:00
Duration: 1 min 46 s
Channel: Sriram Soundarrajan
Description: In Exercises 37-54, find the limit (if it exists). limx →1^- (-1)/((x-1)^2)

step 1 today we are going to solve problem number 38 from limits and continuity here it's like minus 1

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

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Key Concepts

One-Sided Limits

One-sided limits focus on the behavior of a function as the variable approaches a particular point exclusively from one side (either from the left or the right). They are essential when the function behaves differently on either side of the point, helping in understanding abrupt changes or discontinuities in the function.

Limit of a Function

This concept involves finding the value that a function approaches as the variable gets arbitrarily close to some specific point. It is a fundamental idea in calculus, serving as the basis for defining continuity, derivatives, and integrals.

Behavior Near Vertical Asymptotes

When a function’s denominator approaches zero, the function may exhibit infinite behavior, indicating the presence of a vertical asymptote. Studying these behaviors is key to comprehending the limits that approach infinity or negative infinity as the function becomes unbounded near these points.

Impact of Squaring on Function Behavior

Squaring a term in the denominator guarantees a non-negative result, regardless of the sign of the original expression. This property simplifies the analysis of limits, as it ensures the term's impact on the sign and magnitude of the function is predictable, especially when the variable is close to the critical value where the squared term vanishes.

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