Find lim x - 0-sgnx-lim x - 0-sgnx- where sgnx represents the signum function

Sgn (x) gives the sign of x That is If x gt; 0 sgn (x)=1 If x lt; 0 sgn (x)= 1 and If x = 0 sgn (x)=0 So the graph of sgn (x) will look like lim_x→ 0 ...

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Standard XII

Mathematics

Non Removable Discontinuities

Find lim x → ...

Question

$F i n d lim x \to 0 + s g n (x) + lim x \to 0 - s g n (x), w h e r e s g n (x)$ represents the signum function
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Solution

sgn (x) gives the sign of x

That is If x > 0 $s g n (x) = 1$

If x < 0 $s g n (x) = - 1$

and If x = 0 $s g n (x) = 0$

So the graph of sgn (x) will look like

$lim x \to 0 + s i g n (x)$ is the value of sign (x) as x approaches zero from right. We can see from graph that it is 1.

$lim x \to 0 - s i g n (x)$ is the value of sign (x) as x approaches zero from reft. We can see that the value is -1.

$\Rightarrow a n s w e r = 1 + (- 1) = 0$

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Findlimx→ 0+sgn(x)+limx→ 0−sgn(x), where sgn(x) represents the signum function ___

$F i n d lim x \to 0 + s g n (x) + lim x \to 0 - s g n (x), w h e r e s g n (x)$ represents the signum function
___