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

If $f\left(x_{0}, y_{0}\right)=3,$ what can you say about$$\lim _{(x, y) \rightarrow\left(x_{0}, y_{0}\right)} f(x, y)$$if $f$ is continuous at $\left(x_{0}, y_{0}\right) ?$ If $f$ is not continuous at $\left(x_{0}, y_{0}\right) ?$ Give reasons for your answers.

limit will not exist.

Calculus 3

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Oregon State University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

00:34

If $f\left(x_{0}, y_{0}\ri…

02:33

00:40

Suppose that $ \lim_{(x, y…

01:34

If $\lim _{x \rightarrow 0…

01:02

$$\begin{array}{l}…

00:47

If $f$ is a continuous fun…

01:01

01:42

If $f(x)$ is continuous at…

02:31

Explain why $f$ is not con…

01:22

If $\lim _{(x, y) \rightar…

06:08

01:16

Let$$f(x)=\left\{\begi…

looking at this question, something that we know is that the function Excellent wine ice equal to three. And we want to see what we can say about the limit as ex wise approaching this point of f of x y and two different cases. First, about this continuous at this point, and secondly, if it is not continuous, so for suppose this continuous no, it's not. Then clearly the limit as X Y goes Teo. Excellent wine. I'm if X Y is equal to three and we just know this from technicians and everything. If it's continuous there, then clearly the limit will just equal to three. Since we're playing in these points for X and Y. However, if if it's not continuous, then we don't really know much about the value of the function. At that point, when we were taking the limit, the limit I could have any value different from three not really just depends on the type of this continuity there, but if you have any value different from three or the limit may not even exist at that point,

View More Answers From This Book

Find Another Textbook

03:59

Boston and New York are approximately 280 miles apart. One train leaves Bost…

03:01

Solve for the unknown, and then check your solution.$$\frac{2}{3} x=8$$<…

Rewrite the equation in the form $a x^{2}+b x+c=0,$ with $a > 0,$ and the…

01:58

Find the unknown.$$(6 y-2)^{2}+9=41$$

02:07

Solve for the indicated variable.$$\text { For } x: a x+b y=c$$

01:04

03:17

Two angles are said to be complementary if the sum of the measures of their …

01:27

01:14

Complete the square in each of the following by putting in the form $(x+B)^{…

01:55

In each of the following exercises, solve the given inequality.$$(x-3)(x…