Solution: Each of Exercises 75–78 gives a function ƒ(x, y)
Chapter 13, Problem 78E(choose chapter or problem)
Each of Exercises 75–78 gives a function \(f(\mathrm{x}, \mathrm{y}, \mathrm{z})\) and a positive number \(\epsilon\). In each exercise, show that there exists a \(\delta>0\) such that for all \((\mathrm{x}, \mathrm{y}, \mathrm{z})\),
\(\sqrt{x^{2}+y^{2}+z^{2}}<\delta \Rightarrow|f(x, y, z)-f(0,0,0)|<\epsilon\).
\(f(x, y, z)=\tan ^{2} x+\tan ^{2} y+\tan ^{2} z, \quad \epsilon=0.03\)
Equation Transcription:
ƒ(x, y, z)
(x, y, z)
Text Transcription:
ƒ(x, y, z)
epsilon
delta ＞ 0
(x, y, z)
sqrt x^2+y^2+z^2 < delta right double arrow |f(x,y,z)-f(0, 0, 0)| < epsilon
f(x, y, z) = tan^2 x + tan^2 y + tan^2 z, epsilon = 0.03
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