Show that the function `f(x)` given by `f(x)={((e^(1/x)-1)/(e^(1/x)+1), when x!=0), (0, when x=0):}` is discontinuous at `x=0` .

Explanation

To show that the function \( f(x) \) is discontinuous at \( x = 0 \), we need to check the limit of \( f(x) \) as \( x \) approaches 0 and compare it with the value of \( f(0) \).

The function is defined as:
\[
f(x) =
\begin{cases}
\frac{e^{1/x} - 1}{e^{1/x} + 1} & \text{when } x \neq 0 \\
0 & \text{when } x = 0
...