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Find the limit or show that it does not exist. …

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Problem 17 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to -\infty}\frac{x - 2}{x^2 + 1} $


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02:40

Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Related Topics

Limits

Derivatives

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Top Calculus 1 / AB Educators
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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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Watch More Solved Questions in Chapter 2

Problem 1
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Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
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Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
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Problem 47
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Problem 75
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Problem 80
Problem 81

Video Transcript

So here we are asked to evaluate specific limit. So we're asked to evaluate a limit as X approaches negative infinity of x minus two over x squared plus one. So with large numbers uh the constant terms are going to become in uh insignificant. So we can ignore the -2 in the plus one. So this would just be the limit as X approaches negative infinity of X divided by x square. So we can eliminate an X. So this would be one over X. For now we're just evaluating the limit as X approaches negative infinity of one over X and we can apply direct substitution here. So this would be negative one over infinity and we know that one over infinity is just to zero in this case. We could have also evaluated this by law rule where we would be taking the derivative of the numerator and the derivative denominator. So the derivative of the numerator would be one, The derivative of the Dye, Romney would be two x. So we would have to apply once again direct substitution in this case. So 1/2 times negative infinity would once again also be zero. So this gives two different ways for evaluating this limit and this is our final answer

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Calculus: Early Transcendentals

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Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Catherine Ross

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Anna Marie Vagnozzi

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Heather Zimmers

Oregon State University

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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