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Category: Limits

Question-89882

Question Number 89882 by student work last updated on 19/Apr/20 Answered by Joel578 last updated on 19/Apr/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}!\left(\mathrm{1}−\:{x}\:−\:\mathrm{1}\right)}{\left(\mathrm{2}{x}−\mathrm{1}\right){x}!}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{−{x}}{\mathrm{2}{x}−\mathrm{1}}\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by TANMAY…

Question-89712

Question Number 89712 by thor123 last updated on 18/Apr/20 Commented by mathmax by abdo last updated on 18/Apr/20 $${lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{x}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }{{x}−\mathrm{2}}\:=\frac{−\mathrm{2}^{\mathrm{2}} }{−\mathrm{2}}\:=\mathrm{2} \\ $$…

is-lim-x-a-f-x-lim-x-a-f-x-

Question Number 89576 by M±th+et£s last updated on 18/Apr/20 $${is}\:\:\underset{{x}\rightarrow{a}} {{lim}}\lfloor{f}\left({x}\right)\rfloor=\lfloor\underset{{x}\rightarrow{a}\:} {{lim}}\:{f}\left({x}\right)\rfloor\: \\ $$ Commented by mr W last updated on 18/Apr/20 $${i}\:{think}\:{no}. \\ $$$${example}\:{f}\left({x}\right)=\frac{\mathrm{sin}\:{x}}{{x}}…

lim-x-0-cos-x-2-1-x-4-2-x-2-x-sin-x-2-

Question Number 89540 by M±th+et£s last updated on 17/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{cos}\left({x}^{\mathrm{2}} \right)−\mathrm{1}+\frac{{x}^{\mathrm{4}} }{\mathrm{2}}}{{x}^{\mathrm{2}} \left({x}−{sin}\left({x}\right)\right)^{\mathrm{2}} } \\ $$ Commented by abdomathmax last updated on 17/Apr/20 $${let}\:{f}\left({x}\right)=\frac{{cos}\left({x}^{\mathrm{2}}…