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

Explain in your own words the meaning of each of the following.

(a) $ \displaystyle \lim_{x \to \infty} f(x) = 5 $(b) $ \displaystyle \lim_{x \to - \infty} f(x) = 3 $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Ma. Theresa Alin

Numerade Educator

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

01:19

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Pio H.

February 22, 2021

Can the graph of y=f(x) intersect a vertical asymptote? can it intersect a horizontal asymptote? illustrate by sketching graphs.

Missouri State University

Oregon State University

Harvey Mudd College

Idaho State University

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

Explain in your own words …

01:17

02:13

Writing Describe in your o…

02:46

Explain the meaning of eac…

02:54

02:19

$$\text { Explain the mean…

03:13

Write a formal definition …

for this problem, we are to explain the meaning of each of the following statement. The first one is the limit of F of X as X approaches infinity equals five, and The other one is the limit of the function. As X approaches negative infinity equals three. Now, for the first one, since X approaches infinity, then it tells us that we are moving far to the right and we're looking at the value the function varied approaches to and since this is equal to five, then as we move far right, the value of the function approaches to five. Because X approaches an infinite value, The value of F of X can never equal five. It will only approach it. And so we can say that the function Has a horizontal sm so that y equal to five. Now for the 2nd 1, since we're approaching negative infinity, then we're moving far to the left. And so as you move far to the left, the value of the function approaches 23 And because X approaches negative infinity, Then the value of F of X can never equal to three. It will only approach it. Hence we can say that F of X has a horizontal essent. Oh, dad, Why equal to 3?

View More Answers From This Book

Find Another Textbook

01:35

.There are 16 boys and 24 girls. If they will be grouped separately in teams…

02:17

the length of a rectangular floor is 5m longer than its width.The area of th…

04:09

Learning Task 3: Arrange the following sets of numbers in increasing order. …

00:59

A car travels 180 m the first minute, 250 m the next minute, 320 m the third…

01:22

When three times a number is divided from nine the answer is three and when …

03:41

Set up an equation and solve. One leg of a right triangle is 10m less than …

01:06

What is the percentage by mass of 24 grams calcium carbonate mixed with anot…

01:26

if 270kg of corn would feed 42 horses for 21 days for how many days would 36…

02:31

The semicircle of area 1250 pi centimeters is inscribed inside a rec…

01:07

The fare F of a passenger varies directly as the distance d of his destinati…