Problem

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

View

Problem 31 Easy Difficulty

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty} \frac{x^4 - 3x^2 + x}{x^3 - x + 2} $

Answer

$\infty$

Watch More Solved Questions in Chapter 2

Problem 1

Problem 2

Problem 3

Problem 4

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

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Video Transcript

all right, we want to find a limit of this expression as X approaches positive infinity. Since X is going to be approaching positive infinity, it's going to be positive and it's going to be very large and then larger and even larger. So when we look at the numerator, X to the fourth minus three X squared plus x. Even though we have three terms uh as X gets very very large uh one of these terms, the one with the highest power is going to be the dominant term, so the numerator is going to be dominated by extra fourth uh because as X is very large, exit 1/4 will be extremely large three times X to the second won't be anywhere near uh you know, as large as X to the fourth. So even though we're subtracting three X squared uh this whole numerator really is going to be dominated by the highest power backs D x to the fourth term. Likewise, the denominator is going to be not is going to be dominated by the X to the third term. So this entire expression is basically going to be dominated by X to the 4th over X to the third as X approaches positive infinity Now exit the 4th divided by extra 3rd is really x. Okay, so as X approaches positive infinity. This entire expression is basically going to behave as the value of X itself would. So it's X gets a very very large X or this expression this limit is also going to get very very large. So as X approaches infinity, we expect this function to approach infinity. Here on the graph. I have the function graft. And you can clearly see that as as X approaches positive infinity, the function is approaching positive infinity. Okay, we can zoom out and you can see the more and more you move to the right as X approaches positive infinity are the function is getting higher and higher. So as X approaches positive infinity, our function approaches positive infinity, and that's why our function has an infinite limit. The limit of our function as X approaches infinity is infinity.

Leon D.

Temple University

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Problem