Question Number 158327 by Tawa11 last updated on 02/Nov/21 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\:\:\:\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{1}\:\:\:+\:\:\:\mathrm{x}^{\mathrm{n}} }\:\:\:\:\mathrm{does}\:\mathrm{not}\:\mathrm{converge}\:\mathrm{uniformly}\:\mathrm{on}\:\:\left[\mathrm{0},\:\:\mathrm{2}\right] \\ $$$$\mathrm{by}\:\mathrm{showing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{function}\:\mathrm{is}\:\mathrm{not}\:\mathrm{continuous}\:\mathrm{on}\:\:\:\:\left[\mathrm{0},\:\:\mathrm{2}\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92785 by Ar Brandon last updated on 09/May/20 $$\left.\mathrm{a}\left.\right)\:\mathrm{Find}\:\mathrm{E}\left(\mathrm{x}^{\mathrm{x}} \right)\:\mathrm{then}\:\mathrm{E}\left(\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \right)\:\mathrm{for}\:\mathrm{x}\in\right]\mathrm{0},\mathrm{1}\left[\right. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{find}\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{E}\left(\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \right) \\ $$ Commented by Ar Brandon…
Question Number 92782 by device4438043516@gmail.com last updated on 23/May/20 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92741 by john santu last updated on 09/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{2}}{\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:+\:\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{cos}\:\left(\mathrm{x}\right)\right)}\right)\:= \\ $$ Commented by abdomathmax last updated on 09/May/20 $${yes}\:{yes}\:…{i}\:{will}\:{delet}\:{the}\:{post}\:…{nevermind}… \\ $$…
Question Number 92729 by M±th+et+s last updated on 08/May/20 $${if}\:{p}_{{n}} \:{is}\:{the}\:{product}\:{of}\:{the}\:{terms}\:{in} \\ $$$${the}\:{nth}\:{row}\:{of}\:{the}\:{pascal}'{s}\:{triangle} \\ $$$${find} \\ $$$$\underset{{n}\rightarrow\infty} {{lim}}\frac{{p}_{{n}−\mathrm{1}} {p}_{{n}+\mathrm{1}} }{\left({p}_{{n}} \right)^{\mathrm{2}} } \\ $$$$ \\…
Question Number 27189 by abdo imad last updated on 02/Jan/18 $${let}\:{give}\:{S}_{{n}\:} =\:\sum_{{p}=\mathrm{1}} ^{{p}={n}} \:{arctan}\:\left(\frac{\mathrm{1}}{\mathrm{2}{p}^{\mathrm{2}} }\:\right)\:\:{find}\:{lim}_{{n}−>\propto} \:{S}_{{n}} \:\:. \\ $$ Answered by prakash jain last updated…
Question Number 27153 by abdo imad last updated on 02/Jan/18 $${find}\:{the}\:{value}\:{of}\:\prod_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:{sin}\left(\frac{{k}\pi}{\mathrm{2}{n}}\:\right)\:. \\ $$ Commented by abdo imad last updated on 03/Jan/18 $${let}\:{introduce}\:{the}\:{polynomial}\:{p}\left({x}\right)=\:{x}^{\mathrm{2}{n}} \:−\mathrm{1}\:\:{the}\:{roots}\:{of}\:{p}\left({x}\right)…
Question Number 158204 by tounghoungko last updated on 01/Nov/21 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{sin}\:\sqrt{{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}\:}\right)\:=? \\ $$ Answered by ajfour last updated on 01/Nov/21 $${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}2cos}\:\left(\frac{\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}}{\mathrm{2}}\right)\mathrm{sin}\:\left(\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}}}{\mathrm{2}}\right) \\ $$$$=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}2cos}\:\left(\frac{\frac{\mathrm{1}}{\:\sqrt{{h}}}+\frac{\sqrt{{h}+\mathrm{1}}}{\:\sqrt{{h}}}}{\mathrm{2}}\right)\mathrm{sin}\:\left(\frac{\frac{\sqrt{{h}+\mathrm{1}}−\mathrm{1}}{\:\sqrt{{h}}}}{\mathrm{2}}\right)…
Question Number 158205 by tounghoungko last updated on 01/Nov/21 $$\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({e}^{{x}} −\mathrm{1}\right)\mathrm{sin}\:{x}+\mathrm{tan}\:^{\mathrm{3}} {x}}{\mathrm{arctan}\:{x}\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{4}{x}\right)+\mathrm{4arcsin}^{\mathrm{4}} \:{x}}\: \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}+\mathrm{ln}\:\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{2}{x}\right)+\mathrm{2arcsin}\:^{\mathrm{3}} \:{x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{4}{x}+\mathrm{sin}\:^{\mathrm{2}} {x}} \\ $$ Terms of Service…
Question Number 158203 by tounghoungko last updated on 01/Nov/21 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{n}}.{e}^{\frac{\mathrm{2}{k}+\mathrm{1}}{{k}}} \:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com