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Problem

Find the horizontal and vertical asymptotes of ea…

02:53

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Problem 49 Easy Difficulty

Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes.

$ y = \dfrac{2x^2 + x - 1}{x^2 + x -2} $


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02:41

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
Grace He
Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

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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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 24
Problem 25
Problem 26
Problem 27
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Problem 32
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Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
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Problem 41
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Problem 43
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Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
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Problem 61
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Problem 65
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Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
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Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81

Video Transcript

for this problem we want to find the horizontal and vertical sm totes of the curve. Why equal to two X squared plus x minus one over X squared plus x minus two for the horizontal s in total to find it. We would take the limit of the function or the curve as X approaches positive and negative infinity. And so from here we have Why equal to the limit? As X approaches plus minus infinity of two, x squared plus X -1 over Extra Plus X -2. Now, since we're dealing with limits of infinity then we would factor out the variable, the highest exponent for the numerator and variable with the highest exponents for the denominator. And so and here we have the limit as X approaches plus, remind us infinity of we have x squared times two plus one over x minus one over X squared this all over X squared times we have one plus one over x minus two over x squared simplifying We have limit as X approaches plus or minus infinity of two plus one over x minus one over x squared this divided by one plus one over x -2 over x squared. Now evaluating at infinity we have two Plus 1 over plus minus infinity minus. We have plus or minus infinity over one plus 1 over plus, remind us infinity minus two over plus or minus infinity. Now constant over infinity will always approach zero And so this term of is zero. So as this one also this one and this one and so we are left with 2/1 or two. Therefore our horizontal sm toad Is y equal to two. How to find the vertical ascent. Oh, it was simply Set the denominator equal to zero and solve for X. That means we solve for expert plus X minus two equals zero. Now we can factor this and we have X Plus two times X -1. This is equal to zero and this will give us Exports to equal zero Or X -1 equals zero. This is just x equals negative two and X equals one. Therefore the vertical essen toads are X equals -2 and X equals one. Over here we have the graph of the function and from here we can see that the horizontal sm toad is indeed Y equals two. And the vertical lesson toads are X equals negative two And this one is x equals one.

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Related Topics

Limits

Derivatives

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Grace He

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Lectures

Video Thumbnail

04:40

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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.

Join Course
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