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Category: Limits

Question-46007

Question Number 46007 by Meritguide1234 last updated on 19/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 21/Oct/18 $${T}_{{k}} =\mathrm{1}−{tan}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{2}^{{k}} }\right) \\ $$$$\:\:\:\:\:=\left\{\mathrm{1}−{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}^{{k}} }\right)\right\}\left\{\mathrm{1}+{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}^{{k}}…

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

Question Number 111528 by bemath last updated on 04/Sep/20 $$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\:\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{cos}\:\mathrm{x}} \:? \\ $$ Answered by bobhans last updated on 04/Sep/20 $$\mathrm{let}\:\mathrm{1}−\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{w}\:;\:\mathrm{where}\:\mathrm{w}\rightarrow\mathrm{0}\:\mathrm{and}\:\mathrm{sin}\:\mathrm{x}=\mathrm{1}−\mathrm{w} \\…

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Question Number 111498 by bemath last updated on 04/Sep/20 $$\:\:\:\:\:\:\sqrt{\mathrm{bemath}\:} \\ $$$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{3}\:}]{\mathrm{2x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} }\:+\:\mathrm{x}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)^{\frac{\mathrm{1}}{\mathrm{sin}\:\pi\mathrm{x}}} \:? \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\mathrm{x}^{\mathrm{2}} } {\int}}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{dt}\:=\:\mathrm{x}\:\mathrm{cos}\:\left(\pi\mathrm{x}\right)\:.\:\mathrm{Find}\:\mathrm{f}\:\left(\mathrm{4}\right). \\…

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Question Number 111471 by PNL last updated on 03/Sep/20 $${using}\:{power}\:{expension},\:{compute}\:{the}\:{follplowing} \\ $$$${limit}\:{as}\:{a}\:{function}\:{of}\:\alpha>\mathrm{0} \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{{x}^{\frac{\mathrm{7}}{\mathrm{2}}} {ln}\left({x}\right)−{sinh}\left({x}^{\mathrm{2}} \right)+{cosh}\left({ln}\left(\mathrm{1}−\sqrt{\mathrm{2}}{x}\right)\right)−\mathrm{1}}{{x}^{\alpha} } \\ $$ Terms of…

1-lim-x-0-sin-x-ln-e-x-cos-x-x-sin-x-2-lim-x-1-1-x-ln-x-1-2x-x-2-

Question Number 111414 by bobhans last updated on 03/Sep/20 $$\:\left(\mathrm{1}\right)\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{ln}\:\left(\mathrm{e}^{\mathrm{x}} \:\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}\:\mathrm{sin}\:\mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{x}+\mathrm{ln}\:\left(\mathrm{x}\right)}{\mathrm{1}−\sqrt{\mathrm{2x}−\mathrm{x}^{\mathrm{2}} }} \\ $$ Answered by john santu last updated on…

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Question Number 111383 by john santu last updated on 03/Sep/20 $$\:\:\underset{{s}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{20}{s}^{\mathrm{2}} +\mathrm{2}{s}}−\sqrt{\mathrm{5}{s}^{\mathrm{2}} +\mathrm{1}}−\sqrt{\mathrm{5}{s}^{\mathrm{2}} −\mathrm{2}{s}} \\ $$ Answered by bobhans last updated on 03/Sep/20 $$\:\mathrm{L}_{\mathrm{1}}…

bemath-lim-x-x-4x-2-1-x-2-2x-1-

Question Number 111351 by bemath last updated on 03/Sep/20 $$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{x}−\sqrt{\mathrm{4x}^{\mathrm{2}} +\mathrm{1}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}}}\:? \\ $$ Answered by ajfour last updated on 03/Sep/20 $$\:\:\:\:\:=\underset{{x}\rightarrow−\infty}…

bemath-lim-x-0-1-x-sin-1-x-1-x-2-

Question Number 111326 by bemath last updated on 03/Sep/20 $$\:\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{x}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)}\:−\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:\right)\:=? \\ $$ Answered by john santu last updated on 03/Sep/20…