Question Number 31709 by gunawan last updated on 13/Mar/18 $$\mathrm{Given}\:\mathrm{sequence}\:\left({y}_{{n}} \right)\:\mathrm{with}\:{y}_{\mathrm{1}} =\mathrm{1}\:, \\ $$$${y}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{4}}\left({y}_{{n}} ^{\mathrm{3}} +{y}_{{n}} ^{\mathrm{2}} \right)−\mathrm{1}\: \\ $$$$\mathrm{find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{y}_{{n}} \\ $$ Terms…
Question Number 31708 by gunawan last updated on 13/Mar/18 $$\mathrm{Given}\:\mathrm{sequence}\:\mathrm{real}\:\mathrm{function}\:\left({f}_{{n}} \right)\:, \\ $$$${f}_{{n}} :\:\left[\mathrm{0},\:\mathrm{2}\right]\:\rightarrow\:\mathbb{R}\:,\mathrm{with}\: \\ $$$${f}_{{n}} \left({x}\right)=\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}} }\:\:.\:{n}=\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:… \\ $$$$\mathrm{a}.\mathrm{Prove}\:\left({f}_{{n}} \right)\:\mathrm{not}\:\mathrm{uniformly}\:\mathrm{convergent}\:\mathrm{on}\:\left[\mathrm{0},\:\mathrm{2}\right] \\ $$$$\mathrm{b}.\:\mathrm{Find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{f}_{{n}}…
Question Number 31707 by gunawan last updated on 13/Mar/18 $$\mathrm{Find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\Sigma}}\frac{\mathrm{1}}{{n}}\mathrm{sin}\frac{\mathrm{2}\pi}{{n}}\: \\ $$ Commented by abdo imad last updated on 18/Mar/18 $${i}\:{think}\:{the}\:{Q}.{is}\:{find}\:{lim}_{{n}\rightarrow\infty} \:\sum_{{k}=\mathrm{1}}…
Question Number 97238 by bobhans last updated on 07/Jun/20 Commented by john santu last updated on 07/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:^{\mathrm{2}} {x}\:\left(\mathrm{cos}\:^{\mathrm{2}} {x}−\mathrm{1}\right)}{\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\mathrm{4}}−\mathrm{1}\right)\left(\mathrm{1}−\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{2}}−\mathrm{1}\right)}\:= \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 31705 by gunawan last updated on 12/Mar/18 $$\mathrm{Given}\:\mathrm{sequence}\left({x}_{{n}} \right)\:\mathrm{with}\:\mathrm{0}<{a}={x}_{\mathrm{1}} <{x}_{\mathrm{2}} ={b} \\ $$$${x}_{{n}+\mathrm{1}} ={x}_{{n}+\mathrm{1}} +{x}_{{n}} \:,\:{n}=\mathrm{1},\:\mathrm{2},\:\mathrm{3},… \\ $$$$\mathrm{review}\:\mathrm{sequence}\:\left({r}_{{n}} \right)\:\mathrm{with}\:{r}_{{n}} =\frac{{x}_{{n}+\mathrm{1}} }{{x}_{{n}} }\:,\:{n}=\mathrm{1},\:\mathrm{2},\:\mathrm{3},… \\…
Question Number 31706 by gunawan last updated on 13/Mar/18 $$\mathrm{Given}\:\theta_{{n}} =\:{arc}\:\mathrm{tan}\:{n}\:,\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\theta_{{n}+\mathrm{1}} −\theta_{{n}} = \\ $$ Commented by abdo imad last updated on 18/Mar/18 $${if}\:{the}\:{question}\:{is}\:{find}\:{lim}_{{n}\rightarrow\infty}…
Question Number 162775 by john_santu last updated on 01/Jan/22 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{a}\:\mathrm{sin}\:\mathrm{3}{x}\:−\:{b}\:\mathrm{sin}\:\mathrm{2}{x}\:}{{x}^{\mathrm{3}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:{Find}\:{a}\:{and}\:{b}\:. \\ $$ Answered by mr W last updated on 01/Jan/22 $$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 31675 by gunawan last updated on 12/Mar/18 $$\mathrm{calculate}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{cos}\:{x}}{dx} \\ $$ Commented by abdo imad last updated on 12/Mar/18 $${perhaps}\:{there}\:{is}\:{a}\:{error}\:{in}\:{the}\:{Q}.{how}\:{can}\:{have}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}…
Question Number 31676 by gunawan last updated on 12/Mar/18 $$\mathrm{Given}\:\mathrm{function}\:{f}\:\mathrm{diferensiabel}\:\mathrm{on}\:\boldsymbol{\mathrm{R}}. \\ $$$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left(\frac{{a}}{{x}}+{b}\right)\:\mathrm{non}\:\mathrm{zero} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[{f}\left(\frac{{a}}{{x}}+{b}\right)−\frac{{a}}{{x}}{f}'\left(\frac{{a}}{{x}}+{b}\right)\right]={a} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{value}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{f}\left({x}\right) \\ $$ Terms of Service Privacy…
Question Number 31672 by gunawan last updated on 12/Mar/18 $$\mathrm{for}\:\mathrm{what}\:\mathrm{value}\:{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{series} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}}−\mathrm{sin}\:\frac{\mathrm{1}}{{n}}\overset{{p}} {\right)}\:\:\mathrm{convergens}\:? \\ $$ Commented by abdo imad last updated on 12/Mar/18…