Evaluate :
`lim_(x to 0) (e^(cos x)-1)/(cos x)`

Answer

To evaluate the limit \( \lim_{x \to 0} \frac{e^{\cos x} - 1}{\cos x} \), we can follow these steps:

### Step 1: Substitute \( x = 0 \)
We start by substituting \( x = 0 \) into the expression.

\[ \cos(0) = 1 \]

So, we have:

\[ \lim_{x \to 0} \frac{e^{\cos x} - 1}{\cos x} = \frac{e^{\cos(0)} - 1}{\cos(0)} = \frac{e^1 - 1}{1} \]

### Step 2: Simplify the expression
Now, we simplify the expression:

\[ \frac{e - 1}{1} = e - 1 \]

### Final Answer
Thus, the limit evaluates to:

\[ \lim_{x \to 0} \frac{e^{\cos x} - 1}{\cos x} = e - 1 \]