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

Find the limit of $f$ as $(x, y) \rightarrow(0,0)$ or show that the limit does not exist.$$f(x, y)=\frac{x^{2}-y^{2}}{x^{2}+y^{2}}$$

DNE

Calculus 3

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Johns Hopkins University

Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

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

02:31

Find the limit of $f$ as $…

03:10

02:41

02:28

06:23

Find the limit, if it exis…

eso for this limit, we can consider its value. Um, various has a potion s. So, for instance, to assure version one path to consider is along the y axis with wishes with X zero in a new bunch case way have y squared over zero square. That's why Square, which, of course, is the one. And then, alternatively, you consider line X equal toe. Why s so in this case we have Why square No ver y squared? Plus wise. Where in, of course that is up. You know, that's a distinct from one. And a limit. If it existed, would have that be a variant of the Pathan wishes approach. But here we found two different paths. Well, in the Y axis, Well, on the line X is why. And we found through the same values Canada values with all them, respectively. We found by his one and 1/2 and, uh, since they're not equal, then we conclude that the limit does not exist.

View More Answers From This Book

Find Another Textbook

03:03

In each of the following exercises, solve the given inequality.$$x^{2}+x…

03:58

In each of the following exercises, solve the given inequality.$$x^{3}-1…

03:15

Solve each of the quadratics by first completing the square. When the roots …

02:19

In each of the following, solve the given quadratic equation exactly using t…

02:16

Find the slope, $x$ -intercept and $y$ -intercept of the given line.$$4 …

06:15

In each of the following exercises, solve the given inequality.$$(3 x-4)…

02:32

Solve for the unknown, and then check your solution.$$x-7=9$$

03:31

The sum of three consecutive integers is $96,$ find the three integers.

03:29

The length of a rectangle is two feet less than three times its width. If th…

01:26

Determine the equation of the line whose slope and $y$ -intercept are given.…