The limit $\lim _{a \rightarrow 0} \frac{1}{a} \int_{2-a}^{2+a} \cos ^2(\pi t) e^{\left|\frac{2-t}{a}\right|} d t$

• Correct answer
  A

  equals $2(e-1)$
• B

  equals $2(1-e)$
• C

  equals $(e-1)$
• D

  does not exist

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