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

DNE

Calculus 3

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

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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.

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02:31

Find the limit of $f$ as $…

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02:28

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.

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