We want to find the limit of $2^{-x}$ as $x$ approaches infinity. In other words, we need to find $\lim_{x \to \infty} 2^{-x}$.

1. Problem Description

We want to find the limit of $2^{-x}$ as $x$ approaches infinity. In other words, we need to find $\lim_{x \to \infty} 2^{-x}$.

2. Solution Steps

We can rewrite $2^{-x}$ as $\frac{1}{2^x}$.

So, we want to find $\lim_{x \to \infty} \frac{1}{2^x}$.

As $x$ approaches infinity, $2^x$ also approaches infinity. Therefore, we have:

$\lim_{x \to \infty} \frac{1}{2^x} = \frac{1}{\infty} = 0$

3. Final Answer

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