Answer
$\frac{1}{2}$
Work Step by Step
Here we have to find the value of
$\lim\limits_{l \to +\infty} -\frac{1}{2}e^{-x^{2}}$ when $x$ goes from 0 to $l$
In this case, -$\frac{1}{2}$ is a number which is unaffected by the change in the value of $l$ and therefore, our above expression can be written as
$-\frac{1}{2}\lim\limits_{l \to +\infty} e^{-x^{2}}$ when $x$ goes from 0 to $l$
Now, we will change the value of the inner expression,
Value of the inner expression when x = 0 is 1 because $x^{0} = 1$
and the value of inner expression when x = $l$ is $e^{-l^{2}}$
Therefore our expression becomes
$-\frac{1}{2}\lim\limits_{l \to +\infty} (e^{-l^{2}} + 1)$
For $e^{x}$
When x = $\infty$; $e^{-x} =e^{-\infty} = 0 $
Therefore,
Our expression will become
$-\frac{1}{2} (0+1)$ = $\frac{1}{2}$
