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

Prove the statement using the $ \varepsilon $, $ \delta $ definition of a limit.

$ \displaystyle \lim_{x \to a} c = c $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Daniel Jaimes

Numerade Educator

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

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 4

The Precise Definition of a Limit

Limits

Derivatives

Missouri State University

Oregon State University

Harvey Mudd 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.

01:50

Prove the statement using …

01:57

01:59

03:38

02:18

$19-32$ Prove the statemen…

02:17

this problem Number twenty four of this tour Calculus eighth edition Section two point four Prove the statement using the absolute out the definition of a limit The limit is, experts say, of sea. Is he called to see you? Ah, the Epsilon Delta definition of limit is that for any absolute greater than zero there exists a delta greater than zero such that if the absolutely of the difference between exiting is less than a delta, then you have the value of the different between the function and l will be less than absolute. We'LL begin with the second limit and work from there are the second inequality. Second, inequality states that absolutely of the function In this case, the function is seen minus the limit. Tell him it is equal to seem This must be lesson Absalon, if we take C from CC represents a constant value to any content and it's the exact same constant zero and the absurd values here with zero and we get the statement that zeroes less than epsilon. Now what we should do first is we call Absalon is always greater than zero. That was one of our conditions and here and this. Working with the second inequality, we get a statement that is always true because of this case. Absolute skated in zero absolutely great isn't zero. Therefore, we can conclude any Delta choi. Any choice of Delta allows for our statement to be consistent, since regardless of any absolute that we choose, any Delta will be permissible because the statement will always be true and this limit always exists, regardless of choice of the telltale.

View More Answers From This Book

Find Another Textbook

01:24

if an=3+5n then find sum of 24 terms of an A.P

08:33

Two parallel chord PQ and MN are 3cm apart on the same side of a circle wher…

If 30% of a radioactive substance disappears in 10 days, how long will it ta…

03:04

Divide x^5 + 4x^4 – 4x^3 – 10x^2 + 28x – 1 by x^2 + 2x – 3