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Determine the infinite limit.

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

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04:27

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

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.

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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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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