Download the App!

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

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Find the $x$ -values at which the graph in Exercise 36 crosses its horizontal asymptote.

$$x \approx-17.33,-1.577,0.9851,2.424$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:40

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

02:36

Find the $x$ -values at wh…

01:26

Sketch the graph of the fu…

00:38

Determine the horizontal a…

03:10

Find all values of $x$ whe…

00:16

The graph of $y=\frac{3 x-…

And this question we're looking at number 36 is function of Quebec's and we're trying to figure out what X values show the graph going through our horizontal Assen took. So you should have found the horizontal, asked him Toby In question 36 but we'll go through quickly and I'll just go over how we would find that. So we're finding the horizontal S in tow. We're looking at the highest howard X. So we're looking at the coefficient and the X. With the highest exponents. And in this problem you might look and say, oof that means we have to do a bunch of multiplication, lots of really gross time consuming math. But all you actually have to do, we're just worried about these exes. So instead of multiplying everything out, we're just going to figure out what exponents each would have. So this first X is just going to X. Our second X. Here there's a squared. So we're going to make that X squared. And for a third set of parentheses, we have X. But on the outside their square so we'll get an X squared out of that. So you'll notice. I'm not worrying about anything else. Multiplying out. We're just looking at the X is so now in the denominator we have an X and a squared. So we have X squared. And over here we have a two X. So that's going to be two cubed. So eight execute. So now we're going to simplify, we have X to the fifth over eight X to the fifth because we're just adding our exponents Rx M 5th cancel and we get 1/8. So our horizontal smt is why equals wanting. So really we're looking and saying all right of Ilex, It was 18 and we just wanted to see when that equals our function. So this will help us find our X values. Now don't panic. You're not going to be able to solve this. Doing algebra. So what you're gonna want to do is using graphing calculator or something online that will do that And you'll graph y equals 1/8 and then why equals your function here? And you're going to find all of the intersections between the two different lines. So when you do that, You'll get x approximately negative 17.33 Native 1.577 .9851 And 2.424. So these problems where you're looking at intersections, you're just going to want to figure out what values you're looking at and then find a way to either graph it or if you can do the algebra, solve it, doing the algebra to find your values. So these are the four places where The two are going to cross over.

View More Answers From This Book

Find Another Textbook

Numerade Educator

03:58

Let $y=a x^{2}+b x+c .$ Find the slope of the chord (see Exercises 34 and 35…

01:05

The line $y=m x+b$ is called a slant or oblique linear asymptote of the func…

03:21

Find the $x$ -values at which the graph in Exercise 36 crosses its horizonta…

01:12

Use the first and second derivatives to sketch the graph of the given equati…

02:02

01:53

If $f(x)=a_{5} x^{5}+a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x+a_{0},$ fin…

01:04

(a) What happens to the product rule if $F(x)=S(x) ?$ (b) Derive a product r…

02:48

02:37

Find the equation of the tangent line to the curve at the given $x$ -value.<…

03:27

A manufacturer of small glass figurines discovers that it costs $1,800$ for …