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(a) Find the vertical asymptotes of the function …

07:58

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Problem 43 Hard Difficulty

Determine the infinite limit.

$ \displaystyle \lim_{x \to 0}(\ln x^2 - x^{-2}) $


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Daniel Jaimes

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Related Topics

Limits

Derivatives

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Top Calculus 1 / AB Educators
Grace He
Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Problem 16
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Problem 55

Video Transcript

to evaluate this limit, know that we can rewrite this into limit as X approaches zero of you have to Ln of x minus one over x rays to the second power. This is because Ln of a reached um is the same as M Elena V property of natural log. And then from here evaluating at zero we get to Ln of zero minus 1/0 squared and from here we have two times negative infinity. Since the value of natural log as X approaches zero approaches negative infinity and then you have minus 1/0, which will always approach positive infinity as X goes to zero either from the left or right, so this is minus infinity and we have negative infinity minus negative infinity. This will give us evaluations negative infinity. Therefore the value of the limit is negative infinity.

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Calculus: Early Transcendentals

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Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Join Course
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