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Category: Limits

Question-73251

Question Number 73251 by aliesam last updated on 09/Nov/19 Answered by mind is power last updated on 09/Nov/19 $$\mathrm{E}\left(\mathrm{u}_{\mathrm{n}} \right)\leqslant\mathrm{u}_{\mathrm{n}} <\mathrm{E}\left(\mathrm{u}_{\mathrm{n}} \right)+\mathrm{1}=\mathrm{U}_{\mathrm{n}+\mathrm{1}} \\ $$$$\Rightarrow\mathrm{U}_{\mathrm{n}} \mathrm{is}\:\mathrm{a}\:\mathrm{creasing}\:\mathrm{squances}…

lim-x-0-tan-picos-2-x-sin-2pisin-2-x-

Question Number 138767 by bramlexs22 last updated on 18/Apr/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\pi\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{sin}\:^{\mathrm{2}} {x}\right)}\:=? \\ $$ Answered by EDWIN88 last updated on 18/Apr/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\pi\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\right)}{\mathrm{sin}\:\left(\mathrm{2}\pi\mathrm{sin}\:^{\mathrm{2}}…

lim-0-0-lim-0-

Question Number 73223 by malwaan last updated on 08/Nov/19 $$\boldsymbol{{lim}}\:\frac{\mathrm{0}}{\infty}\:\overset{?} {=}\:\mathrm{0}\:? \\ $$$$\boldsymbol{{lim}}\:\frac{\infty}{\mathrm{0}}\:\overset{?} {=}\:\infty\:? \\ $$ Commented by MJS last updated on 08/Nov/19 $$\mathrm{these}\:\mathrm{are}\:\mathrm{not}\:\mathrm{of}\:\mathrm{correct}\:\mathrm{syntax}\:\Rightarrow\:\mathrm{we}\:\mathrm{cannot} \\…

Question-73117

Question Number 73117 by aliesam last updated on 06/Nov/19 Commented by mathmax by abdo last updated on 06/Nov/19 $${we}\:{have}\:{cos}\left(\mathrm{3}{x}\right)\sim\mathrm{1}−\frac{\left(\mathrm{3}{x}\right)^{\mathrm{2}} }{\mathrm{2}}\:\:\left({x}\rightarrow\mathrm{0}\right)\:\Rightarrow{cos}\left(\mathrm{3}{x}\right)−\mathrm{1}\:\sim−\frac{\mathrm{9}{x}^{\mathrm{2}} }{\mathrm{2}}\:\Rightarrow \\ $$$$\mathrm{1}−{cos}\left(\mathrm{3}{x}\right)\sim\frac{\mathrm{9}{x}^{\mathrm{2}} }{\mathrm{2}}\:\Rightarrow\frac{\mathrm{1}−{cos}\left(\mathrm{3}{x}\right)}{{x}^{\mathrm{2}} }\sim\frac{\mathrm{9}}{\mathrm{2}}\:\Rightarrow{lim}_{{x}\rightarrow\mathrm{0}}…