How do I show that $\frac{1}{x^{2/x}} \to 1$ as $x\to\infty$? From looking at the graph, it looks like this function converges to 1 as $x\to\infty$. But with mathematical rigours, how would I show this? 

$$\lim _{ x\rightarrow \infty  }{ { x }^{ -\frac { 2 }{ x }  } } =\lim _{ x\rightarrow \infty  }{ { e }^{ -\frac { 2 }{ x } \ln { x } \quad \quad  } } \overset { L'Hospital }{ = } \lim _{ x\rightarrow \infty  }{ { e }^{ -\frac { 2 }{ x }  } } =1$$
