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Question-170551




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

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