# How do you prove that the curves of #y=x^x# and y = the Functional Continued Fraction (FCF) generated by #y=x^(x(1+1/y))# touch #y=x#, at their common point ( 1, 1 )?

##### 1 Answer

Aug 27, 2016

The curves intersect without osculating.

#### Explanation:

Considering

Those functions intersect at clearly at

Now the tangency at this point obeys

So they intersect without osculating.