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

Name: Problem 41, Chapter 1: Calculus of a Single Variable
Uploaded: 2020-11-03T03:53:18-08:00
Duration: 2 min 32 s
Channel: Samuel Goyette
Description: In Exercises 37-54, find the limit (if it exists). limx →1^+ (x^2)/((x-1)^2)

step 1 In this problem, we have a limit. So the limit as x get closer to 1 from the positive side of x

Question

In Exercises $37-54,$ find the limit (if it exists). $$ \lim _{x \rightarrow 1^{+}} \frac{x^{2}}{(x-1)^{2}} $$

   In Exercises $37-54,$ find the limit (if it exists).
$$
\lim _{x \rightarrow 1^{+}} \frac{x^{2}}{(x-1)^{2}}
$$

Calculus of a Single Variable

Ron Larson, Bruce… 9th Edition

Chapter 1, Problem 41

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Solved by Expert Samuel Goyette

11/03/2020

Step 1

This means we are considering values of $x$ that are slightly greater than $1$. Show more…

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In Exercises $37-54,$ find the limit (if it exists). $$ \lim _{x \rightarrow 1^{+}} \frac{x^{2}}{(x-1)^{2}} $$

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Key Concepts

Limit

A limit describes the behavior of a function as its input approaches a particular value. It is a foundational concept in calculus that helps in understanding the value that the function is approaching, even if that value is not actually reached at the point of interest.

One-Sided Limit

A one-sided limit focuses on how a function behaves as the variable approaches a target value from one side only—either from the left or the right. This is critical when the function exhibits different behaviors depending on the direction of approach, especially around points of discontinuity.

Infinite Limit

An infinite limit occurs when the function's values increase or decrease without bound as the input approaches a certain value. This concept is often used to describe the behavior of functions near vertical asymptotes where the function diverges to infinity.

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