If $f(t)=\int_{-t}^t \frac{e^{-|x|}}{2} d x$, then $\lim _{t \rightarrow \infty} f(t)$ is equal

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Aicharya · Accepted Answer

$\begin{aligned} f(t) & =\int_{-t}^t \frac{e^{-|x|}}{2} d x \ & =2 \int_0^t \frac{e^{-x}}{2} d x \ & =-\left[e^{-x}ight]_0^t=-e^{-t}+1\end{aligned}$ Now, $\begin{aligned} \lim _{t ightarrow \infty} f(t) & =-\lim _{t ightarrow \infty} e^{-t}+1 \ & =0+1 \ & =1\end{aligned}$

If $f(t)=\int_{-t}^t \frac{e^{-|x|}}{2} d x$, then $\lim _{t \rightarrow \infty} f(t)$ is equal

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