Question Number 46330 by Saorey last updated on 24/Oct/18 $$\mathrm{pls}\:\mathrm{help}\:\mathrm{me}! \\ $$$$\mathrm{L}=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{13}}]{\mathrm{x}}−\sqrt[{\mathrm{7}}]{\mathrm{x}}}{\:\sqrt[{\mathrm{5}}]{\mathrm{x}}−\sqrt[{\mathrm{3}}]{\mathrm{x}}} \\ $$ Commented by MJS last updated on 24/Oct/18 $$\mathrm{I}\:\mathrm{would}\:\mathrm{again}\:\mathrm{recommend}\:\mathrm{l}'\mathrm{Hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{1}}…
Question Number 46187 by annika0209 last updated on 22/Oct/18 $$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}×\mathrm{n}^{\frac{\mathrm{1}}{\mathrm{n}}} }=?\:\:\:\:\:\:\:\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}!!!! \\ $$$$ \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 46146 by Sanjarbek last updated on 21/Oct/18 Commented by Meritguide1234 last updated on 21/Oct/18 $${e}^{\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx}} \\ $$ Commented by Meritguide1234…
Question Number 46136 by Meritguide1234 last updated on 21/Oct/18 Answered by ajfour last updated on 21/Oct/18 $$\left(\mathrm{cos}\:{nx}\right)^{\mathrm{1}/{n}} \:=\:\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \:\frac{{nx}}{\mathrm{2}}\right)^{\mathrm{1}/{n}} \\ $$$$\:\:\:\:\:{if}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:{then}\:\:=\:\mathrm{1}−\frac{\mathrm{2}}{{n}}\left(\frac{{n}^{\mathrm{2}} {x}^{\mathrm{2}} }{\mathrm{4}}\right) \\…
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Question Number 46007 by Meritguide1234 last updated on 19/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 21/Oct/18 $${T}_{{k}} =\mathrm{1}−{tan}^{\mathrm{4}} \left(\frac{\pi}{\mathrm{2}^{{k}} }\right) \\ $$$$\:\:\:\:\:=\left\{\mathrm{1}−{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}^{{k}} }\right)\right\}\left\{\mathrm{1}+{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}^{{k}}…
Question Number 111528 by bemath last updated on 04/Sep/20 $$\:\:\:\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 $$\mathrm{let}\:\mathrm{1}−\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{w}\:;\:\mathrm{where}\:\mathrm{w}\rightarrow\mathrm{0}\:\mathrm{and}\:\mathrm{sin}\:\mathrm{x}=\mathrm{1}−\mathrm{w} \\…
Question Number 111498 by bemath last updated on 04/Sep/20 $$\:\:\:\:\:\:\sqrt{\mathrm{bemath}\:} \\ $$$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{3}\:}]{\mathrm{2x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} }\:+\:\mathrm{x}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)^{\frac{\mathrm{1}}{\mathrm{sin}\:\pi\mathrm{x}}} \:? \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\mathrm{x}^{\mathrm{2}} } {\int}}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{dt}\:=\:\mathrm{x}\:\mathrm{cos}\:\left(\pi\mathrm{x}\right)\:.\:\mathrm{Find}\:\mathrm{f}\:\left(\mathrm{4}\right). \\…
Question Number 111471 by PNL last updated on 03/Sep/20 $${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…
Question Number 111442 by bobhans last updated on 03/Sep/20 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{x}+\mathrm{a}}{\mathrm{x}−\mathrm{a}}\right)^{\mathrm{x}} ? \\ $$ Answered by bemath last updated on 03/Sep/20 Answered by ajfour last…