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Each of Exercises $59-62$ gives a function $f(x, y)$ and a positive number $\epsilon .$ In each exercise, show that there exists a $\delta>0$ such that for all $(x, y),$$$\sqrt{x^{2}+y^{2}}<\delta \Rightarrow|f(x, y)-f(0,0)|<\epsilon$$$$f(x, y)=y /\left(x^{2}+1\right), \quad \epsilon=0.05$$

$\epsilon=0.05$

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, we are given that f o x y is equals toe by our X squared plus one and a positive real number at Salon is it was toe 0.5 and we have to show that Delta is greater than zero for all such that X Goma y and Underwood X squared plus y square is less than data and more off fo x y minus. F 00 is less than Absalon. Now Let their basic was 20.5 Then more off X is less than data and more of why is less than data We get model fo x y minus fo 00 is equals toe model bio our X squared less one minus zero. We get more off by or X square plus one, please less than equal do more off. Why less than 0.0 is equals toe epsilon. Therefore, the solution is epsilon is equals tau 0.5

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