Question Number 170551 by 2407 last updated on 26/May/22
Answered by JDamian last updated on 26/May/22
$$\mathrm{3} \\ $$
Answered by Rasheed.Sindhi last updated on 26/May/22
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −\mathrm{6}\mid{x}\mid}{{x}^{\mathrm{2}} −\mathrm{2}\mid{x}\mid} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mid{x}\mid^{\mathrm{2}} −\mathrm{6}\mid{x}\mid}{\mid{x}\mid^{\mathrm{2}} −\mathrm{2}\mid{x}\mid} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\cancel{\mid{x}\mid}\left(\mid{x}\mid−\mathrm{6}\right)}{\cancel{\mid{x}\mid}\left(\mid{x}\mid−\mathrm{2}\right)} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mid{x}\mid−\mathrm{6}}{\mid{x}\mid−\mathrm{2}}=\frac{\mathrm{0}−\mathrm{6}}{\mathrm{0}−\mathrm{2}}=\mathrm{3} \\ $$