Question

Solve $\underset{x\to 0}{lim}\frac{x}{\left|x\right|}=?$

Answer 1

We have,

$\underset{x\to 0}{lim}\frac{x}{\left|x\right|}$

We know that

$\left|x\right|=x,ifx>0$

$\left|x\right|=-x,ifx<0$

Therefore,

$\underset{x\to 0^{+}}{lim}\frac{x}{x}$

$\underset{x\to 0^{+}}{lim}\left(1\right)$

$=1$

Similarly,

$\underset{x\to 0^{-}}{lim}\frac{x}{(-x)}$

$\underset{x\to 0^{-}}{lim}(-1)$

$=-1$

Hence, this is the answer.