Question

How do you find the limit of `rootx(x)` as `x>oo`?

Answer 1

`lim_(x->oo) root(x)x =1`

Explanation:

We can write `f(x) = root(x)x` as:

`f(x) = root(x)x = (x^(1/2))^(1/x)=x^(1/(2x))=e^(lnx/(2x))`

so, as:

`lim_(x->oo) lnx/(2x)=0`

`lim_(x->oo) root(x)x = lim_(x->oo)e^(lnx/(2x))= e^0=1`

graph{root(x)x [-0.75, 19.25, -4.88, 5.12]}