Evaluate the following limits :
`lim_(x to -infty)e^(x)`

Answer

To evaluate the limit \( \lim_{x \to -\infty} e^x \), we can follow these steps:

### Step 1: Understand the behavior of the function
As \( x \) approaches \(-\infty\), we need to analyze what happens to the expression \( e^x \).

### Step 2: Rewrite the limit
We can express the limit as:
\[ \lim_{x \to -\infty} e^x = e^{-\infty} \]

### Step 3: Evaluate \( e^{-\infty} \)
The exponential function \( e^x \) approaches 0 as \( x \) approaches \(-\infty\). Therefore:
\[ e^{-\infty} = 0 \]

### Step 4: Conclude the limit
Thus, we can conclude that:
\[ \lim_{x \to -\infty} e^x = 0 \]

### Final Answer:
\[ \lim_{x \to -\infty} e^x = 0 \]

---