- #1
Ahmes
- 78
- 1
Hello,
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 of k the 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.
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 of k the 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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