Provide an appropriate response.We say that a function f(x, y, z) approaches the limit L as (x, y, z) approaches (x0, y0, z0) and write 
f(x, y, z) = Lif for every number ? > 0, there exists a corresponding number ? > 0 such that for all 
in the domain of f, 
Show that the 
requirement in this definition is equivalent to
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What will be an ideal response?
The sphere centered at (x0, y0, z0) of radius ? circumscribes the cube centered at 
and with sides 
Therefore, 
and 
imply 
Likewise, the cube centered at 
with sides 2? circumscribes the sphere with radius ?. Thus, 
implies 
and 
The requirements are equivalent.
Mathematics
src="https://sciemce.com/media/4/ppg__10615191621__f1q268g5.jpg" alt="" style="vertical-align: -8.0px;" />
What will be an ideal response?
The sphere centered at (x0, y0, z0) of radius ? circumscribes the cube centered at and with sides Therefore, and imply Likewise, the cube centered at with sides 2? circumscribes the sphere with radius ?. Thus, implies and The requirements are equivalent.
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Fill in the blank(s) with the appropriate word(s).