Question

$Find\underset{x\to 0}{lim}+sgn\left(x\right)+\underset{x\to 0}{lim}-sgn\left(x\right),wheresgn\left(x\right)$ represents the signum function

Answer 1

sgn (x) gives the sign of x

That is If x > 0 $sgn\left(x\right)=1$

If x < 0 $sgn\left(x\right)=-1$

and If x = 0 $sgn\left(x\right)=0$

So the graph of sgn (x) will look like

$\underset{x\to 0}{lim}+sign\left(x\right)$ is the value of sign (x) as x approaches zero from right. We can see from graph that it is 1.

$\underset{x\to 0}{lim}-sign\left(x\right)$ is the value of sign (x) as x approaches zero from reft. We can see that the value is -1.

$\Rightarrow answer=1+(-1)=0$