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If I am given a function of several variables and a parameter. Such as:

[tex]f(x,y,z)=\frac{x y z^2}{(x^2+y^2+z^2)^k}[/tex]

This function is defined to be 0 where it is incontinuous (in [tex](0,0,0)[/tex]).

How can I conclude for which values ofkthe function has three continuous partial derivatives?

I know how to conclude differentiability of the function, but differentiability means partial derivatives exist, not necessarily continuous.

Thank you.

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# Homework Help: [calculus] Continuity of partial derivatives

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