Evaluate-lim-x-0-x-x-

Question Number 80718 by TawaTawa last updated on 05/Feb/20

Evaluate : \lim_{x \to 0} \frac{x}{∣ x ∣}

Commented by mind is power last updated on 05/Feb/20

∣ x ∣= {\begin{cases} x, x > 0 \\ - x, x < 0 \end{cases}

\Rightarrow \lim_{x \to 0^{+}} \frac{x}{∣ x ∣} = \lim_{x \to 0^{+}} = \frac{x}{x} = 1

\lim_{x \to 0^{-}} \frac{x}{∣ x ∣} = \lim_{x \to 0^{-}} \frac{x}{- x} = - 1

\lim_{x \to 0} \frac{x}{∣ x ∣} d o n t e x i s t

Commented by TawaTawa last updated on 08/Feb/20

God bless you sir