the limit of (1+2x)^(1/y) as (x,y) approaches (0,0)

[joi]

I have to evaluate the following limit and I am stuck:

. . .the limit of (1+2x)^(1/y) as (x,y) approaches (0,0)

I think I want to take the natural log of the limit. Then I would have (1/y) * lim(1+2x) as x approaches 0. Is this a good approach to take?

Thanks for any feedback!

 

[pka]

As written, there is no limit. For one thing, the function is not defined for any point on the x-axis. Along the path x=y the limit is e<SUP>2</sup> and along the path x=0 the limit is 1.

 

[joi]

Thanks.