Question

A piecewise function is given by f(x)what is the value of lim f (x)

Answer 1

We will have the following:

We must analyze the limit from left and right, that is:

`\begin{gathered} \lim_(x\to-\pi/2)((2)/(\pi)x)=1 \\ \\ \lim_(x\to+\pi/2)(sin(x))=1 \end{gathered}`

From this, we can see that the limit from left and right seems to approach to 1. Thus:

`\lim_(x\to\pi/2)f(x)=1`