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Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty} \bigl[\ln (2 + x) - \ln (1 + x) \bigr] $

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02:11

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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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find the limit of Ln of two plus x minus Ln of one plus X. As X approaches infinity, we first rewrite this into the limit as X approaches infinity of L N of two plus x over one plus X. And here we use the property of natural log Ln of a minus Ln f b. This is equal to Ellen of a over B and then you sing limit loss for natural log functions. We can rewrite this further into Ln of the limit as extra purchase infinity of two plus X over one plus X. Now factoring out the very well with the highest exponent for the inside of L N. We have Ln limit as X approaches infinity of X times two over X plus one. This all over X times one over X plus one. And from here we have Ln of the limit as X approaches infinity of and here we can cancel out the X and we get two plus X plus one over one plus xbox one. and evaluating its infinity, we have L. N. of two over infinity plus one over one over Infinity Plus one. No constant over infinity. We'll always approach to zero and saw this to over infinity zero As well as one over infinity. And so we have Ln of 1/1. This is equal to Alan of one, that's Equal to zero. And so this is the value of the limits.

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