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Find the limits in Exercises $13-20$ by rewriting the fractions first.$$\lim _{(x, y) \rightarrow(2,-4)} \frac{y+4}{x^{2} y-x y+4 x^{2}-4 x}$$

$\frac{1}{2}$

Calculus 3

Calculus 1 / AB

Chapter 14

Partial Derivatives

Section 2

Limits and Continuity in Higher Dimensions

Applications of the Derivative

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In this problem, you have to find the limits by rewriting the faction. Now it is given that limit. X Y approaches two and minus four, and why is not equal toe? Fall and X is not equal to X square and by, plus pour over X square. Why? Minus X y plus four X squared, minus four X Now the nominator approaches zero as X Y approaches two and minus four now, but simplifying eight limit X Y approaches to minus four. Why is not equal toe? Fall and X is not equal to X square. We will get by plus four over X y Multiply X minus one plus four eggs. Mollify X minus one. We will get limit X Y approaches to minus four where why is not ableto poor and X is not able to x square Really good. Why plus four over X y plus four x Ex finest one Now with spotter simplifying it. We will get limit X Y approaches to minus four, where y is not equal to four and X is not equal to X square. We will get one or x modify X minus one. Now we'll apply the limits limit X Y approaches to minus food. L Y is not equal toe for an X is not equal toe. Explore well, you get one over two multiplied to minus one. We will get 1/2. Therefore, limit X Y approaches to minus four, advising not equal to four and access not ableto X square y plus four over X square Y minus X y plus four X squared minus four X is equal to one hour to that's the solution.

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