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

Decide whether or not the function is continuous. If it is not continuous, identify the points at which it is discontinuous.$$f(x)=\left\{\begin{array}{l}0 \text { if } x<0 \\x \text { if } x \geq 0\end{array}\right.$$

Continuous

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

Missouri State University

Campbell University

Baylor University

University of Nottingham

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.

06:47

Decide whether or not the …

02:01

02:38

02:08

06:48

02:27

02:47

Determine whether or not t…

in discussion or in this problem, we have to decide whether or not the function is continuous. If it is not continuous, we will. We have to identify the points at which it is discontinuous, so the human function is F of X is equal to zero. There's a piece wise function if X is less than zero, and eggs if X is greater than are equal to zero, is the value of the function. F of X is difficult. F of X is equal to zero for when X is less than zero. It means that this function is continuous for all the values of X, which is less than or equal to zero. Similarly F of X is equal to the value of the function is X when X is greater than are equal to zero again. F of X is equal to X is a polynomial, so this will be continuous for all the values of X greater than zero. Now we will check. The continuity of the function at X is equal to Europe, so it for continuity for a function to be continuous, it must satisfy the conditions. The three conditions of the of the function. Yeah, the three conditions that are the the function should be defined at the given point. So f of zero is equal to f of the urological too. We have a pope accessible tracks for X greater than or equal to zero. So f of zero is equal to zero for X is equal to zero. So the given function is define at X is equal to zero. Now we will check the We will check whether the limit exists at X radical 20 or not. So, first of all, we will find the left and side limit, So limit X approaches to zero from left hand side of the function as X is less than zero because X approaches to zero from left hand side, it means that access less than zero. So from the function, the value of the function is zero when X is less than zero. So we have zero now the right hand side limit. Now we will try to find the right hand side limit, so limit X approaches to zero from right hand side. Therefore, effects as X approaches to zero from right hand side. It means that X is greater than zero. So from that function we have, the value of the function is X. When X is less, the X is greater than zero. So this implies that we have on applying limit. We have zero again, so left hand side limit is equal to right hand side limit. So this implies that limit X approaches to zero f of X is exist. And finally the third condition is this is the second condition, and the third condition for the continuities limit of the function at the given point should be equal to the value of the function at that point. So limit X, brought just during f of X is equal to zero because left hand side limit and right hand side limit is equal. So we have lim X approaches to zero f of X is equal to zero and the value of the function at X is equal to zero is also zero. Yeah, so all the properties of the continuity is satisfied by the human function. So we can say that the human function is continuous everywhere

View More Answers From This Book

Find Another Textbook

01:37

Find $\frac{d}{d x}\left(\frac{3}{x^{2}}\right)$ by (a) using the power rule…

04:48

Plot each of the following lines on the same set of axes. (a) $y=2 x$(b)…

01:23

Determine the horizontal asymptotes, if they exists.$$f(x)=\frac{2 x^{2}…

02:10

Determine the coordinates of the midpoint of the line segment joining the po…

02:43

a) sketch the graph of the given function, and then draw the tangent line at…

02:00

Given the curve whose equation is $f(x)=\sqrt{x+4} .$ Let $P$ be the point(5…

02:32

(a) Find the $x$ -intercept(s); (b) Find the vertical asymptotes; (c) Find t…

01:41

Use the appropriate rules to determine the derivative.$$f(x)=2 x^{7}-\fr…

02:22

02:55

Find the point on the curve $y=x^{3}$ at which the tangent line at (2,8) cro…