Question Number 142140 by gsk2684 last updated on 26/May/21
![[lim_(x→0) ((sin x)/x)]=? lim_(x→0) {[((100sin^(−1) x)/x)]+[((100tan^(−1) x)/x)]}=? lim_(x→0) {[((100x)/(sin^(−1) x))]+[((100x)/(tan^(−1) x))]}=? where [x] denotes greatest integer less than or equal to x. solution please](Q142140.png)
$$\left[\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{{x}}\right]=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100sin}^{−\mathrm{1}} {x}}{{x}}\right]+\left[\frac{\mathrm{100tan}^{−\mathrm{1}} {x}}{{x}}\right]\right\}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\left[\frac{\mathrm{100}{x}}{\mathrm{sin}^{−\mathrm{1}} {x}}\right]+\left[\frac{\mathrm{100}{x}}{\mathrm{tan}^{−\mathrm{1}} {x}}\right]\right\}=? \\ $$$${where}\:\left[{x}\right]\:{denotes}\:{greatest}\:{integer}\: \\ $$$${less}\:{than}\:{or}\:{equal}\:{to}\:{x}. \\ $$$${solution}\:{please} \\ $$
Answered by mathmax by abdo last updated on 27/May/21
![lim_(x→0) ((sinx)/x)=1 ⇒[lim_(x→0) ((sinx)/x)]=1](Q142158.png)
$$\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{sinx}}{\mathrm{x}}=\mathrm{1}\:\Rightarrow\left[\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{sinx}}{\mathrm{x}}\right]=\mathrm{1} \\ $$
Commented by gsk2684 last updated on 27/May/21
$$\mathrm{thank}\:\mathrm{you} \\ $$