If `f(x)=e^(x)+2x`, then `f(ln 2)=`

Options

A. `1.20`
B. `2.69`
C. `2.77`
D. `3.39`

Explanation

To solve the problem, we need to evaluate the function \( f(x) = e^x + 2x \) at \( x = \ln 2 \).

### Step-by-Step Solution:

1. **Substitute \( \ln 2 \) into the function**:
\[ f(\ln 2) = e^{\ln 2} + 2(\ln 2) \]

2. **Use the property of exponents and logarithms**:
The property states that \( e^{\ln x} = x \). Therefore, we can simplify \( e^{\ln 2} \):
\[ e^{\ln 2} = 2 \]
So, we can rewrite the function:
\[ f(\ln 2) = 2 + 2(\ln 2) \]

3. **Calculate \( 2(\ln 2) \)**:
We know that \( \ln 2 \) is approximately \( 0.693 \). Thus:
\[ 2(\ln 2) \approx 2 \times 0.693 = 1.386 \]

4. **Combine the results**:
Now, substitute back into the equation:
\[ f(\ln 2) = 2 + 1.386 = 3.386 \]

5. **Round to two decimal places**:
The final answer rounded to two decimal places is:
\[ f(\ln 2) \approx 3.39 \]

### Final Answer:
\[ f(\ln 2) \approx 3.39 \]