Question Number 55641 by gunawan last updated on 01/Mar/19 $$\mathrm{Studies}\:\mathrm{of}\:\mathrm{convergences} \\ $$$$\mathrm{the}\:\mathrm{numbers}\:\mathrm{real}\:\mathrm{sequence}\:\left\{{x}_{{n}} \right\}, \\ $$$$\mathrm{with}\:{x}_{\mathrm{1}} =\mathrm{1}\:\mathrm{and}\:{x}_{{n}+\mathrm{1}} =\frac{{x}_{{n}} ^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}_{{n}} },\:{n}\geqslant\mathrm{1} \\ $$$$ \\ $$$$ \\…
Question Number 55639 by gunawan last updated on 01/Mar/19 $$\mathrm{Known}\:{a}\:\in\:\mathbb{R}\:\mathrm{and} \\ $$$$\mathrm{function}\:{f}\::\:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{satiesfied} \\ $$$$\mid{xf}\left({x}\right)+{a}\mid\:<\:\mathrm{sin}^{\mathrm{2}} \:\left({x}−{a}\right).\: \\ $$$$\mathrm{For}\:\mathrm{all}\:{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:{f}\left({x}\right)\:.. \\ $$ Answered by kaivan.ahmadi…
Question Number 55637 by gunawan last updated on 01/Mar/19 $$\mathrm{Value}\:\mathrm{of}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{2}{x}^{{n}} }{{x}+{x}^{\mathrm{2}{n}+\mathrm{1}} }\:{dx}=.. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 01/Mar/19 $$\int_{\mathrm{0}}…
Question Number 121172 by benjo_mathlover last updated on 05/Nov/20 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{x}+\mathrm{1}}{\mathrm{x}+\mathrm{1}}\:? \\ $$$$ \\ $$ Answered by TANMAY PANACEA last updated on 05/Nov/20 $$\underset{{x}\rightarrow\infty}…
Question Number 55635 by gunawan last updated on 01/Mar/19 $$\mathrm{Series}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\Sigma}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }=.. \\ $$ Commented by Joel578 last updated on 01/Mar/19 $${Ans}\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\…
Question Number 55634 by gunawan last updated on 01/Mar/19 $$\mathrm{If}\:\underset{{x}\rightarrow{c}} {\mathrm{lim}}\:\frac{{a}_{\mathrm{0}} +{a}_{\mathrm{1}} \left({x}−{c}\right)+{a}_{\mathrm{2}} \left({x}−{c}\right)^{\mathrm{2}} +…+{a}_{{n}} \left({x}−{c}\right)^{{n}} }{\left({x}−{c}\right)^{{n}} }=\mathrm{0} \\ $$$$\mathrm{then}\:{a}_{\mathrm{0}} +{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +..+{a}_{{n}} =.. \\…
Question Number 55592 by gunawan last updated on 27/Feb/19 $$\underset{{x}\rightarrow\pi/\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}−\mathrm{sin}\:\frac{\pi}{\mathrm{6}}}{\frac{\pi}{\mathrm{6}}−\frac{{x}}{\mathrm{2}}}=.. \\ $$ Commented by maxmathsup by imad last updated on 27/Feb/19 $${let}\:{A}\left({x}\right)=\frac{{cosx}−{sin}\left(\frac{\pi}{\mathrm{6}}\right)}{\frac{\pi}{\mathrm{6}}−\frac{{x}}{\mathrm{2}}}\:\Rightarrow\:{A}\left({x}\right)=\mathrm{6}\frac{{cosx}−\frac{\mathrm{1}}{\mathrm{2}}}{\pi−\mathrm{3}{x}}\:=\mathrm{3}\:\:\frac{\mathrm{2}{cosx}−\mathrm{1}}{\mathrm{3}\left(\frac{\pi}{\mathrm{3}}−{x}\right)} \\ $$$$=\frac{\mathrm{1}−\mathrm{2}{cosx}}{{x}−\frac{\pi}{\mathrm{3}}}\:\:\:{changement}\:{x}−\frac{\pi}{\mathrm{3}}\:={t}\:{give}\:{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{3}}}…
Question Number 186659 by cortano12 last updated on 08/Feb/23 $${find}\:{the}\:{value}\:{a}\:{and}\:{b}\:{if}\: \\ $$$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{2}} }\:+{a}+\frac{{b}}{{x}^{\mathrm{2}} }\right)=\mathrm{0} \\ $$ Commented by mr W last updated on 08/Feb/23…
Question Number 121074 by bramlexs22 last updated on 05/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}? \\ $$ Answered by liberty last updated on 05/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}+\mathrm{1}\right)}}\:=\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\sqrt{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}}\:=\:\mathrm{0} \\…
Question Number 186580 by qaz last updated on 06/Feb/23 $$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{x}^{\mathrm{2}} } {dx}={A}\:\:,{Find}\:\underset{{n}\rightarrow\infty} {{lim}n}\left[\frac{\mathrm{1}}{{n}}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\int_{\mathrm{1}} ^{{i}/{n}} {e}^{{x}^{\mathrm{2}} } {dx}+\frac{{e}−\mathrm{1}}{\mathrm{2}}\right]=? \\ $$ Terms of…