Questions: k(x)=e^(2x)-e^(4x)

Transcript text: 24. $k(x)=e^{2 x}-e^{4 x}$

Solution

Solution Steps

To solve the function $ k(x) = e^{2x} - e^{4x} $, we can evaluate it for specific values of $ x $ or analyze its behavior. For instance, we might want to find the value of $ k(x) $ at a particular point, or determine where it equals zero. The solution involves substituting the desired $ x $ values into the function and computing the result.

Step 1: Evaluate $ k(1) $

To find the value of the function $ k(x) = e^{2x} - e^{4x} $ at $ x = 1 $, we substitute $ x = 1 $ into the function:

\[ k(1) = e^{2 \cdot 1} - e^{4 \cdot 1} = e^{2} - e^{4} \]

Step 2: Calculate $ e^{2} $ and $ e^{4} $

Using the approximate values of $ e^{2} $ and $ e^{4} $:

\[ e^{2} \approx 7.3891 \quad \text{and} \quad e^{4} \approx 54.5982 \]

Step 3: Compute $ k(1) $

Now, we can compute $ k(1) $:

\[ k(1) = 7.3891 - 54.5982 \approx -47.2091 \]