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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




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

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