Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Find the limit or show that it does not exist.

$ \displaystyle \lim_{x \to \infty}\frac{3x - 2}{2x + 1} $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Stark Ledbetter

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

02:39

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Missouri State University

Oregon State University

Boston College

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.

0:00

Find the limit or show tha…

02:04

01:25

01:37

04:19

04:21

Evaluate the limit, if it …

All right. We've got this limit problem. Um We want to find this limit or show that it does not exist. A couple different ways of doing this. Some people like to do uh low petals rule because it's fast. Um I don't like that because limits have to exist before derivatives do. Um Some people like to think about and behavior that's not terrible. Um Actually, if X is growing, I just like to stop it from growing because I don't know what big really big over really big is and that's what we have right now. Um So I'm just gonna make it small. I'm going to divide top and bottom by X. So three x divided by X. three. Um And now I have two times one over X. And then two X divided by X. Two. And then I have one times one over X. And then the only theorem I need for ex growing is as X gets big one over X gets small. You agree with that one divided by a really huge Number is always going to be zero. So then I can plug that theorem into these limits. Right? Um limits can add subtract multiply as long as everything exists. So I have three minus two times zero. Because that thing is going to be zero. When X is big divided by two plus zero. So I'm going to get three minus two times zero divided by two plus zero is 3/2. I think that's the cleanest way to think about this

View More Answers From This Book

Find Another Textbook

00:19

Apply the distributive property to factor out the greatest common factor.45e…

01:07

A van can carry 385 boxes of oranges weighing 25 kg each, whereas another va…

01:45

The principal RS. A, borrowed at As per annum simple interest, for A months …

01:11

The sum of three angles of a quadrilateral is 5 times the fourth angle. Find…

00:58

9. Calculate the perimeter of a rectangle whose area is 25x2 – 35x + 12. Use…

00:57

A fish tank has 240 quarts of water. Levi adds another 120 quarts to the tan…

01:41

a student multiplied 3432 by 72 instead of multiplying it by 27.How much gre…

04:57

find the ratio in which the y axis divides the line segment joining the poin…

01:23

a car is priced at $7200. The car dealer allows a customer to pay a one thir…

01:32

Compare the fraction given below4 upon 5 , 5 upon 7