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Determine the infinite limit.

$ \displaystyle \lim_{x \to 5^-}\frac{x+1}{x-5} $

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02:39

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Harvey Mudd College

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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Hello. We have a question in which we need to determine the limit in finite limit limit. X approaches to file from left side X plus one by that's minus five. So we can see that when we substitute X equal to fight directly here. It will become zero. And will the limit will opposed to infinity. But one thing to be very sure that this is less than five axes less than five. So this will be approaching two zero but it will become less than zero. So there should be minus infinity. So they should approach to minus infinity. This is an answer. But if we draw a graph of this this is X. This is why so definitely X equal to fibers. They're simple. So this is x equal to five. X equal to five is the s in total and this is the particular now degrees of numerator and denominator are the same. So why all to one will be there horizontally is in total? Why call to one will be there horizontal lesson. Tote now. Okay now to the other graph we have to get the X intercept and the Y intercept. If you plug in if you take Michael to X plus one by X minus five to get tax interested. We have to Right? Why Porto Zeros were accepted to -1. This is -1 should be the eccentricity and for my intercept you have to plug in X equal to zero. So minus one by five should be the hawaii interested. So like this. The gulf must look like this. So this is the graph. Now we can easily observe that can we approach this graph? This is actually going to five from this side, so graph is approaching two in minus infinity. So minus infinity should be the correct answer. Thank you.

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