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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) .$$$f(x, y)=\frac{x^{4}}{x^{4}+y^{2}}$$Graph cannot copy

the function 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 were given that function X Y is it was too extra the power forward or extra power forward, less vice. Where now the object is to show that the function has no limits as X Y approaches 00 by considering different parts off approach now, the limit cannot be found by direct substitution because this yields 0/0. So we examined by first part limit X y approaches 00 extra, about four export over actual about four. That's why square is equals to limit X approaches. Zero. Expert About four. Our off zero will get limit X approaches zero X to the power forward for the four. We really get one now, considering the second part limit X y approaches 00 x to the power four or X to the power of or less Y square leg moderate X Approaches. Zero at the par four or extra power four plus X square full square. We will get Lim X approaches. Zero extra about four or actually about four doesn't about four. No well good limit X approaches zero X to the power four or two extra power for, and they will get 1/2. Therefore, the function has no limits as X Y approaches 00 So that's the solution

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