Question Number 133923 by bemath last updated on 25/Feb/21
![lim_(x→0) ((∣sin x∣)/x^2 ) =?](https://www.tinkutara.com/question/Q133923.png)
$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mid\mathrm{sin}\:\mathrm{x}\mid}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$
Answered by EDWIN88 last updated on 25/Feb/21
![x^2 = ∣x∣^2 ⇒ lim_(x→0) ((∣sin x∣)/(∣x∣)) .(1/(∣x∣))= lim_(x→0) ∣((sin x)/x)∣.(1/(∣x∣)) = 1×∞ = ∞](https://www.tinkutara.com/question/Q133924.png)
$$\:\mathrm{x}^{\mathrm{2}} \:=\:\mid\mathrm{x}\mid^{\mathrm{2}} \:\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mid\mathrm{sin}\:\mathrm{x}\mid}{\mid\mathrm{x}\mid}\:.\frac{\mathrm{1}}{\mid\mathrm{x}\mid}=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mid\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\mid.\frac{\mathrm{1}}{\mid\mathrm{x}\mid} \\ $$$$\:=\:\mathrm{1}×\infty\:=\:\infty\: \\ $$