Questions: Evaluate the function at the given value of (x). Round to 4 decimal places if necessary. [ f(x)=e^x ; f(-2) ] 0.1353 0.6931 -5.4366 6.5809

Solution Steps

To evaluate the function \( f(x) = e^x \) at \( x = -2 \), we need to compute the value of the exponential function at this point. We will use Python's math library to calculate the value of \( e^{-2} \) and then round the result to 4 decimal places.

We need to evaluate the function \( f(x) = e^x \) at \( x = -2 \). This gives us: \[ f(-2) = e^{-2} \]

Using the value of \( e \) (approximately \( 2.7183 \)), we compute: \[ e^{-2} \approx \frac{1}{e^2} \approx \frac{1}{(2.7183)^2} \approx 0.1353 \]

The calculated value \( 0.1353352832366127 \) is rounded to four decimal places, resulting in: \[ f(-2) \approx 0.1353 \]

Final Answer