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

(a) Determine the $x$ -intercepts, (b) the vertical asymptotes, (c) the horizontal asymptotes and (d) Sketch the graph of the function whose equation is $f(x)=\frac{8 x^{3}-2 x+3}{4 x^{3}-5 x^{2}+1}$

(a) $x=0.83585$(b) $x=1, \frac{1 \pm \sqrt{17}}{8}$(c) $y=2$$(d)$

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

Boston College

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.

05:48

(a) Determine the $x$ -int…

04:09

(a) Find the $x$ -intercep…

03:04

08:03

02:15

02:07

02:10

02:25

02:40

02:32

02:19

02:33

02:28

02:21

02:38

03:33

a. Identify the horizontal…

01:11

For the graph of $y=f(x)$<…

For the following problem, we want to determine the X intercepts the vertical ascent oats. The horizontal, assume totes and then sketch the graph of the function. So we have the F of X is equal to x or eight X cubed minus two X plus three. Yeah. Not going to be divided by four X cubed minus five X squared plus one. Yeah. Looking at this, we identify the X intercept are going to be When this term here is equal to zero. So we can set it equal to zero and see that we'll have this X intercept right here. Um at negative 0.836. And then we also have the vertical ascent tote Which is going to be x equals one. For example, we'll also have the horizontal Jacinto which is much easier to find. That can be the ratio of 8 to 4. That means why equals two will be our horizontal sm two.

View More Answers From This Book

Find Another Textbook

Numerade Educator

06:00

Use linearization to approximate the given quantity. In each case determine …

03:24

Find the dimensions of the largest rectangle whose perimeter is 144 feet.

01:39

Let $f(x)=x^{-2 / 3}$ on the interval $[-1,8] .$ Does $f$ have extrema on th…

01:46

Find two functions $f$ and $g,$ whose composition $f(x)$ ) will result in th…

06:16

Here is another way to derive the quotient rule. Observe that $N(x)=$ $D(x)\…

00:36

The position of an object at any time is given by the equation $s(t)=5 t^{3}…

02:36

Find the points on the curve $y=x^{4}-8 x^{2}+3$ at which the tangent line i…

02:16

Determine the equation of the tangent line at the indicated $x$ -value.$…

01:04

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

01:03

Sketch the graph of a continuous function decreasing on $-5<x<3$ and i…