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Evaluate the limit and justify each step by indic…

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Problem 5 Medium Difficulty

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).

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


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Daniel Jaimes

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 3

Calculating Limits Using the Limit Laws

Related Topics

Limits

Derivatives

Discussion

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Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

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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Watch More Solved Questions in Chapter 2

Problem 1
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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
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Problem 26
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Problem 39
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Problem 45
Problem 46
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Problem 48
Problem 49
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Problem 53
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Problem 55
Problem 56
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Video Transcript

in this problem we are asked to evaluate this limit limit T approaches -2 of T. The 4th -2 over to t squared -3 T Plus two. All right. So first of all, let's just check if we evaluate the denominator With T at -2. That's two times minus two squared minus three times minus two plus two. That is what we'll minus two squared is four times two is eight. Man is a modest. That's plus two times 3 is six plus two. So that's eight and eight. That's 16. Okay, so this is not zero. All right. So we don't have an issue with dividing by zero and having a vertical assam. Tote at minus two. So therefore the first limit law is at the limit of F of X. This little needle here half of X or G fx is limit of Absolutely limit of half of x times one over the limit of G f x. So that means that we now have a limit As T approaches -2 of Do you? The 4th 1 is two over The limit as T approaches -2 of to t squared minus three T plus two. Okay. Yeah, The next one is a polynomial limit law here. Right? Or the limit of a X squared plus bx. We'll see is is what is the constant? They can come out in front limit X squared plus B times the limit of X. Since he's a constant can come out front was a limit of C which is just see by the way. Okay, so that means I now have The limit as T approaches -2 of T to the 4th minus two over. The limit is two times the limit as T approaches minus two of t squared -3 times the limit as t approaches -2 of T plus two on the end. Okay, so evaluating each one of these limits, well, the limit of this polynomial is just Just going to be this number. Interview that ponytails, that's -2 to the fourth, homelessness to over two times A -2. Is that polonium? It's -2 squared -3 times -2. That's too. And so what do I get? Well minus to the fourth, that's 16 minus two, That's 14 over. We just calculated this to be 16 And so this is 7/8, isn't it? In reduced form.

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Calculus: Early Transcendentals

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Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

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.

Join Course
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