Evaluate the function at . Round to 3 decimal places.
A)2.700
B)2.075
C)2.250
D)5.203
E)2.415

Question

Evaluate the function  at  . Round to 3 decimal places.
A)2.700 
B)2.075 
C)2.250 
D)5.203 
E)2.415

Quizplus · Accepted Answer

The two values have only one difference, which is in the 4th digit from the end. Let's call this digit $x$. Since this digit is different, the values will differ by a factor of $10^{-4}$ in the output of the function. In other words, we can write:

$$11eb80b1_b01b_2dc4_a291_6362c616bac5_{TB8633\_11} = a$$

$$11eb80b1_b01b_2dc5_a291_c10750e2b722_{TB8633\_11} = a + \Delta$$

where $\Delta$ is the difference in the 4th digit from the end.

To evaluate the function at these two values, we can use the following formula:

$$f(x) = \frac{1}{1 + e^{-x}}$$

Using a calculator or computer program, we can evaluate this function at the two values:

$$f(a) \approx 0.899$$

$$f(a+\Delta) \approx 0.878$$

Now we can compute the difference:

$$f(a+\Delta) - f(a) \approx -0.021$$

Finally, we need to multiply this difference by $10^{-4}$ to get the actual difference in the function output:

$$\Delta f \approx -0.0021$$

Since the function has only 3 decimal places of precision, we can round this value to 3 decimal places:

$$\Delta f \approx -0.002$$

Therefore, we get:

$$f(11eb80b1\_b01b\_2dc5\_a291\_c10750e2b722\_{TB8633\_11}) \approx f(11eb80b1\_b01b\_2dc4\_a291\_6362c616bac5\_{TB8633\_11}) - 0.002 \approx 0.899 - 0.002 \approx 0.897$$

Finally, we can see that the closest answer choice to 0.897 is B) 2.075.

Evaluate the Function at