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Determine the infinite limit.

$ \displaystyle \lim_{x \to 2^-}\frac{x^2 - 2x}{x^2 - 4x + 4} $

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03:03

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

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 the limits of x squared minus two. X over x squared minus four, X plus four. As X approaches to from the left, we would rewrite this into the limit as X approaches to from the left of X Times X -2. This all over X -2 Squared. And then from here we can simplify, we can get rid of x minus two and we have Limit as X approaches to from the left of X over we still have X -2 in the denominator. Now, if we plug in two to this function we have to over 2 -2, that's two over zero. Now, if X approaches to from the left then the values of X we are looking at are those X values less than two. So if X is less than two, this means that X -2 will be less than zero. That means The value of X -2 as X approaches to from the left would be a small negative number And so the value of X over X -2 would be a negative infinite number. Therefore this is equal to negative infinity.

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