Question Number 44085 by rk last updated on 21/Sep/18
![lim x→0 [((sin ∣x∣)/x)]](https://www.tinkutara.com/question/Q44085.png)
$${lim}\:\mathrm{x}\rightarrow\mathrm{0}\:\left[\frac{\mathrm{sin}\:\mid{x}\mid}{{x}}\right] \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18
Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18
$${graph}\:{of}\:{sin}\mid{x}\mid \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18
Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18
$${graph}\:{of}\:\frac{{sin}\mid{x}\mid}{{x}} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18
Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18
![lim_(x→0+) [((sin∣x∣)/x)]→1 [.]←greatest integer function lim_(x→0−) [((sin∣x∣)/x)]→−1 so left hand side limit→−1 right hand side limit→1 so limit does not exist](https://www.tinkutara.com/question/Q44157.png)
$$\underset{{x}\rightarrow\mathrm{0}+} {\mathrm{li}{m}}\:\left[\frac{{sin}\mid{x}\mid}{{x}}\right]\rightarrow\mathrm{1}\:\left[.\right]\leftarrow{greatest}\:{integer}\:{function} \\ $$$$\underset{{x}\rightarrow\mathrm{0}−} {\mathrm{lim}}\:\left[\frac{{sin}\mid{x}\mid}{{x}}\right]\rightarrow−\mathrm{1} \\ $$$${so}\:{left}\:{hand}\:{side}\:{limit}\rightarrow−\mathrm{1} \\ $$$${right}\:{hand}\:{side}\:{limit}\rightarrow\mathrm{1}\:\:{so}\:{limit}\:{does}\:{not}\:{exist} \\ $$