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Category: Limits

lim-x-pi-2-2-1-sin-x-2-cos-2-x-

Question Number 138996 by bramlexs22 last updated on 21/Apr/21 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}−\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}{\:\sqrt{\mathrm{2}}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\:=? \\ $$$$ \\ $$ Answered by EDWIN88 last updated on 21/Apr/21 $$\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{sin}\:\mathrm{x}}{\:\sqrt{\mathrm{2}}\left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}\right)}.\underset{{x}\rightarrow\pi/\mathrm{2}}…

lim-x-1-7-x-3-1-3-3-x-2-x-1-

Question Number 138997 by bramlexs22 last updated on 21/Apr/21 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{7}+\mathrm{x}^{\mathrm{3}} }−\sqrt{\mathrm{3}+\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}−\mathrm{1}}=? \\ $$ Answered by EDWIN88 last updated on 21/Apr/21 $$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} \left(\mathrm{7}+\mathrm{x}^{\mathrm{3}}…

Question-138959

Question Number 138959 by mathlove last updated on 20/Apr/21 Answered by mathmax by abdo last updated on 20/Apr/21 $$\mathrm{a}^{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \:=\mathrm{e}^{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{loga}} \:\sim\mathrm{1}+\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{loga}\:\mathrm{and} \\…

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} \\…