Use a graph to find the following limit. $$ \lim _{x \rightarrow \infty} e^{-x} $$

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1. Consider the function $$ e^{-x} $$. This can also be written as:
   $$
   e^{-x} = \frac{1}{e^x}
   $$

2. As $$ x $$ increases, the exponential function $$ e^x $$ grows very rapidly. This means that its reciprocal, $$\frac{1}{e^x}$$, decreases very rapidly.

3. On the graph of $$ y = e^{-x} $$, you'll notice that as $$ x $$ moves to the right (toward infinity), the curve approaches the horizontal line $$ y = 0 $$ without ever touching it. This horizontal line is known as a horizontal asymptote.

4. Therefore, by observing the graph, we conclude that:
   $$
   \lim_{x \rightarrow \infty} e^{-x} = 0
   $$
As $$ x $$ becomes very large, $$ e^{-x} $$ approaches 0. So, the limit is 0.

Use a graph to find the following limit.

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