3 variable limit of (1+xyz)^(1/(x^2+y^2+z^2)) as (x,y,z) ->

[jazzman]

Hey all!
I'm trying to calculate the following limit:
$\displaystyle \lim_{(x,y,z)\to(0,0,0)}{(1+xyz)^\frac{1}{x^2+y^2+z^2}}$

I tried converting it to spherical coordinates:

$\displaystyle \lim_{r\to{0}}{(1+r^3\sin^2\phi\cos\phi\cos\theta\sin\theta)^{\frac{1}{r^2}}}$

But it doesn't seem to help...

Please help me solve!

 

[jazzman]

Can anyone help me out?
This looks like a $\displaystyle 1^\infty$ indeterminate form which is usually $\displaystyle e$ but it doesn't seem to be the answer in this case!