We will have the following:
We must analyze the limit from left and right, that is:
[tex]\begin{gathered} \lim_{x\to-\pi/2}(\frac{2}{\pi}x)=1 \\ \\ \lim_{x\to+\pi/2}(sin(x))=1 \end{gathered}[/tex]
From this, we can see that the limit from left and right seems to approach to 1. Thus:
[tex]\lim_{x\to\pi/2}f(x)=1[/tex]
