Download the App!

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

Estimate the horizontal asymptote of the function$$ f(x) = \frac{3x^3 + 500x^2}{x^3 + 500x^2 + 100x + 2000} $$by graphing $ f $ for $ -10 \le x \le 10 $. Then calculate the equation of the asymptote by evaluating the limit. How do you explain the discrepancy?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

so $y=3$ is a horizontal asymptote.The discrepancy can be explained by the choice of the viewing window. Try [-100,000,100,000] by [-1,4] to get a graph that lends credibility to our calculation that $y=3$ is a horizontal asymptote.

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

University of Nottingham

Idaho 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.

01:27

$$ \begin{array}{c}{\text …

04:39

Estimate the horizontal as…

05:26

00:50

Find the horizontal asympt…

02:41

Asymptote Behavior How clo…

02:19

06:52

Evaluate $\lim _{x \righta…

00:53

Determine the horizontal a…

this problem over fifty three of the Stuart Calculus eighth edition Section two point six estimate the horizontal, hasn't it? Of the function of alecks equals we execute those five hundred x word divided by the quantity X cube two plus five hundred x squared plus one hundred x plus two thousand by graphing F for X is between negative ten and ten. Then calculate the equation of the aspen took by evaluating the limit. How do you explain the discrepancy? So you take this function, we grabbed it first in this range from NATO ten to ten for axe. Here's an example of we're using a graphing and telling me to do this here in this window, we estimate the horizontal as, um took to be approximately ah y equals one. Seems as though the function approaches one as it gets closer and closer to ten and seems to level off at that point. So way, we say and re estimate that words don't ask until maybe why goals to one regarding the second part. We're going to calculate the limit now particular element as X approaches Infinity Ah, dysfunction three x cubed US five hundred x squared All right, Bye. Excuse me. So you want to x squared? Plus one thousand X? It was two thousand, and we're going to do as we take each term and divide by X cubed, which leaves us, which is three plus five hundred or X. Good bye. One plus five hundred or ex. It's one thousand over X squared class two thousand over X cubed and two properties of limits. We can take the limit of each term individually and his expert infinity. Each of these terms approaches hero, the ones that far over the form one over x Adar, where are is irrational value greater than zero and that leaves us with element equals two, three. And what that tells us is that our horizontal Lassiter is actually goes to three. So the discrepancy is there to drew planning. We estimated the horizontal hasn't turned out quite close to one where, as the actual Aspen to isa y equals three and the discrepancy has to do with there using a large enough graf or not understanding the scope of the graph anymore, because on their plant, the function could have increased way more, which it indeed does farther down to X axis in the negative and positive direction. And it indeed we'LL reach Ah! Oh, well, approach Quantico three whenever reach or echo three. Therefore, that is what explains the discrepancy.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:51

'What is the probability that a randomly selected person from this stud…

02:08

"HELP PLSSSSSSSS!!!! I’ll MARK YOU BRAINLY!!! AND NO LINK PLSSSSS!!! TH…

01:45

'Classify triangle ABC. Justify your classificationThe 3 circles th…

01:10

'Find the measure of angle b.Find the measure ofangle b 35)499 …

03:44

"Write the following paragraph proof as a two-column proof.Given: a…

02:06

"pls help quickly . with explanationA salad dressing recipe uses 12…

00:33

'mWhich object is the result of rotating the triangle about line m?…

01:33

"PLEASE HELP??????????????????????????????????Weighted AverageA…

02:21

'9. Find the values of x and y that make these triangles congruent by t…

02:34

'Use the scale factor to find the area of the enlarged figure. Explain …