Question Number 44467 by maxmathsup by imad last updated on 29/Sep/18
$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{{x}^{{n}} {sinx}\:−{sin}\left({x}^{{n}} \right)}{{x}}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 30/Sep/18
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}^{{n}} {cosx}+{sinx}×{nx}^{{n}−\mathrm{1}} −{cos}\left({x}^{{n}} \right)×{nx}^{{n}−\mathrm{1}} }{\mathrm{1}} \\ $$$$=\mathrm{0} \\ $$