Q114 / 160 · TS EAMCET 2007 · Mathematics

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

  • Correct answer
    A
    $1$
  • B
    $\frac{1}{2}$
  • C
    $0$
  • D
    $-1$

Solution

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

Hence, the correct answer is option: 'A'.

Relevant Questions