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By considering different paths of approach, show that the functions in Exercises $35-42$ have no limit as $(x, y) \rightarrow(0,0) .$$$g(x, y)=\frac{x-y}{x+y}$$

As paths, $y=0$ and $x=0$ , give different values for the limit, hence the function$g(x, y)=\frac{x-y}{x+y}$ has no limit as $(x, y) \rightarrow(0,0)$

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 by considering different parts off. Coach needs to be shown that the function that has given G X Y is equals two X minus Y or X plus y has no limits as X Y approaches +00 are considering different parts off approach along XX is where why will be zero. They get limit. X Y approaches 00 x minus Y or X plus y is equals toe limit x zero approaches 00 X minus zero over X plus zero we get limit eggs zero approaches 00 x or x We get limit exceed Oh, approaches 00 one that before we get one now considering part off approach alone, Why exist where X will be zero limit Ex lie approaches 00 x minus Y or x plus y We get limit zero by approaches 00 zero minus y over zero plus y. Now, by solving this, we get limit. Zero vie approaches 00 minus y or by we get minus one. Now, as the parts why is equals to zero and X is equal to give zero give different values for the limit. Hence the function. G X y is supposed to X minus Y or X plus y has no limits as X Y approaches 00 that's a solution.

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