We can clearly see that the graph of $y=x^{\frac{1}{x}}$ is a straight line parallel to x- axis giving a constant value of y =1 for all the values of x.
So when x$\rightarrow \infty$ then also we will get y=1.
$\therefore y= _{ x\rightarrow \infty }^{lim}x^{\frac{1}{x}} = 1$