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
Question Number 27097 by abdo imad last updated on 02/Jan/18 $${let}\:{give}\:\:\:{H}_{{n}} \:=\:\sum_{{k}=\mathrm{1}} ^{{n}\:\:} \:\frac{\mathrm{1}}{{k}}\:\:\:\:{for}\:{p}\:\:{fixed}\:{from}\:\mathbb{N}\: \\ $$$${find}\:\:{lim}_{{n}−>\propto} \:\:{H}_{{n}+{p}} \:\:\:−\:\:{H}_{{n}} \:\:. \\ $$ Commented by prakash jain…
Question Number 27098 by abdo imad last updated on 02/Jan/18 $${let}\:{give}\:{S}\left({x}\right)\:=\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{{x}^{{n}} }{{n}}\:\:{and}\:\:{W}\left({x}\right)=\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{\left(−\mathrm{1}\right)^{{n}} {x}^{{n}} }{{n}^{\mathrm{2}} } \\ $$$${calculate}\:\:\:{S}\left({x}\right).{W}\left({x}\right).\:\:\:{in}\:{that}\:{we}\:{know}\:/{x}/<\mathrm{1}. \\ $$ Commented by…
Question Number 92626 by student work last updated on 08/May/20 Commented by student work last updated on 09/May/20 $$\mathrm{who}\:\mathrm{can}\:\mathrm{solve}? \\ $$ Terms of Service Privacy…
Question Number 92577 by jagoll last updated on 08/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}} \\ $$ Commented by Tony Lin last updated on 08/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{lnx}}{{x}} \\ $$$$=\underset{{x}\rightarrow\infty}…
Question Number 27027 by hoangnampham13 last updated on 01/Jan/18 $${Find}\:{max}\:{and}\:{min}\:{of}\:{the}\:{function}: \\ $$$${f}\left({x}\right)={x}^{\mathrm{2}} {cos}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com