Question Number 170130 by sciencestudent last updated on 17/May/22
$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left(\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)=? \\ $$
Commented by cortano1 last updated on 17/May/22
$$\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({x}−\mathrm{sin}\:{x}\right)\left({x}+\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{2}} \:\mathrm{sin}\:^{\mathrm{2}} {x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{3}} }\:.\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}+\mathrm{sin}\:{x}}{{x}} \\ $$$$=\:\mathrm{2}×\:\frac{\mathrm{1}}{\mathrm{6}}=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$
Commented by sciencestudent last updated on 17/May/22
$${I}\:{did}\:{not}\:{understand}! \\ $$
Commented by sciencestudent last updated on 17/May/22
$${Please}\:{solve}\:{describely}. \\ $$