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Each of Exercises $63-66$ gives a function $f(x, y, z)$ and a positive number $\epsilon .$ In each exercise, show that there exists a $\delta>0$ such that for all $(x, y, z)$ ,$$\quad \sqrt{x^{2}+y^{2}+z^{2}}<\delta \Rightarrow|f(x, y, z)-f(0,0,0)|<\epsilon$$$$f(x, y, z)=\frac{x+y+z}{x^{2}+y^{2}+z^{2}+1}, \quad \epsilon=0.015$$

$\epsilon=0.015$

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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it was given that f o X com Abiko Mazie is equal to X plus by policy. A phone a Square plus Vice Square plus the Square plus one let Delta's equals to 0.5 then x more is smaller than data. Why mode is also smaller than Delta on Z. Mood is also smaller than Delta. We get a four x com Abiko matzzie minus fo zero comma, zero comma zero whole more is equals toe Express by policy Born X squared plus y square plus the square plus one. My new zero call more It would be equals toe X plus y plus Z, divided by X squared plus y squared plus the square plus one pull more, which is equals Toe X plus five plus zero or more. It would be equals two x more plus by more plus e mode, which is smaller than 0.5 plus 0.5 plus 0.5 which is equals to 0.15 which is equals to absolute does. The solution is absolutely is equals to 0.15 This is the final answer

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