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

Define $f(0,0)$ in a way that extends $f$ to be continuous at the origin.$$f(x, y)=\ln \left(\frac{3 x^{2}-x^{2} y^{2}+3 y^{2}}{x^{2}+y^{2}}\right)$$

$\ln 3$

Calculus 3

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Johns Hopkins University

Oregon State University

Baylor University

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

02:56

Define $f(0,0)$ in a way t…

00:51

02:48

For the function$$f(x,…

04:40

Continuous extension Defin…

01:12

How can the function$$…

s in this case, we can begin by considering the argument of the Phoenix alone function. Gore's limits commute with continuous functions. Uh, rewriting the argument with the long function? Uh, slightly. We'll have three times x squared plus y squared over X squared plus y squared. But it's expired. Tons. I squared over. Explain puts my sweet Also s o. Of course, we can cancel the explorer Precise squared in the numerator and denominator of the first ad in their convention the lawn function. And then we just have to consider the second that is No, I wish you can rewrite it follows. But uh huh. And then we can simplify this. No, uh, we can see. Uh, it's this expression convert covers 23 on X, my commercial zero. Oh, this is a case because well, that's where it exploded commercially. Zero, huh? Is it possible? Huh? Um, And then their differences both diverge. And so too does the sum reverse a voyage then? Zio s. So we're left with this tartar. Ah, we're going to every last one over one over the square puzzle over the square and said freedom. That's one over. Uh, infinity. So 30 converts agree what this applies to continuously extend on function. F can really define its value with the origin to be the lawn of three. And to summarize. The reason for doing this is that you've seen that the argument to the lung function converted city, since we can redefine eyes excellent converts to the origin. So Carina find value about that. The origin is being the line of one bit of the argument when she gave you just said and shoulders three. In such a definition of death of the origin constitutes a continuance extension of it.

View More Answers From This Book

Find Another Textbook

02:10

Give an equation of the line with the given slope and passing through the gi…

01:52

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

01:35

Find equation for the given line.A horizontal line passing through $(-3,8).$…

02:41

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

01:34

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

02:44

02:38

03:27

In each of the following exercises, solve the given inequality.$$24 x^{2…

03:43

In each of the following exercises, solve the given inequality.$$25 x-x^…

03:00