Question Number 122998 by benjo_mathlover last updated on 21/Nov/20 $$\:{f}:{R}\rightarrow{R}\: \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{{x}^{\mathrm{2}} +\mathrm{2}{mx}−\mathrm{1}\:;\:{x}\leqslant\mathrm{0}}\\{{mx}−\mathrm{1}\:;\:{x}>\mathrm{0}}\end{cases} \\ $$$${if}\:{f}\left({x}\right)\:{is}\:{one}−{one}\:{then}\:{m}\:{lies}\: \\ $$$${in}\:{interval}\: \\ $$$$\left({a}\right)\:\left(−\infty,\mathrm{0}\:\right)\:\:\:\:\:\left({c}\right)\:\left(\mathrm{0},\infty\right) \\ $$$$\left({b}\right)\:\left(−\infty,\:\mathrm{0}\:\right]\:\:\:\:\:\left({d}\right)\:\left[\:\mathrm{0},\:\infty\:\right)\: \\ $$ Terms of…
Question Number 57422 by Abdo msup. last updated on 03/Apr/19 $${let}\:{U}_{{n}} ={n}\:\int_{\mathrm{1}} ^{\pi} \:\frac{{sinx}}{{x}^{{n}} }{dx} \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 57416 by Abdo msup. last updated on 03/Apr/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{2}{x}} ^{\mathrm{4}{x}} \:\:\:\:\frac{{dt}}{{t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{3}} \\ $$$$\left.\mathrm{1}\right){find}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right) \\ $$ Commented by maxmathsup…
Question Number 57413 by Abdo msup. last updated on 03/Apr/19 $${prove}\:{that}\:{ln}\left(\mathrm{1}+{x}\right)>\frac{{arctanx}}{\mathrm{1}+{x}}\:\:\forall{x}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 57414 by Abdo msup. last updated on 03/Apr/19 $${solve}\:\:{y}'\:=\mathrm{2}{y}^{\mathrm{2}} \:+{y}\:\:\:{and}\:{y}\left({o}\right)=\mathrm{1} \\ $$ Commented by kaivan.ahmadi last updated on 03/Apr/19 $${first}\:{we}\:{notice}\:{the}\:{integral} \\ $$$$\int\frac{{dx}}{\mathrm{2}{x}^{\mathrm{2}} +{x}}=\int\frac{{dx}}{{x}\left(\mathrm{2}{x}+\mathrm{1}\right)}=…
Question Number 57411 by Abdo msup. last updated on 03/Apr/19 $${let}\:{f}\left({x}\right)={arctan}\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right) \\ $$$${find}\:{f}^{−\mathrm{1}} \left({x}\right)\:. \\ $$ Commented by maxmathsup by imad last updated on 04/Apr/19…
Question Number 57412 by Abdo msup. last updated on 03/Apr/19 $${let}\:{u}_{{n}} =\mathrm{1}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:+…+\frac{\mathrm{1}}{\:\sqrt{{n}}} \\ $$$${prove}\:{that}\:\left({u}_{{n}} \right)\:{is}\:{divdrgente}. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 57409 by Abdo msup. last updated on 03/Apr/19 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{\mathrm{2}{n}+\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} \:+{k}}} \\ $$$${calculste}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$ Commented by maxmathsup by imad…
Question Number 57410 by Abdo msup. last updated on 03/Apr/19 $${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\frac{{sin}\left({x}^{\mathrm{5}} \:+{x}−\mathrm{2}\right)}{{x}−\mathrm{1}} \\ $$ Commented by maxmathsup by imad last updated on 04/Apr/19 $${in}\:{this}\:{case}\:{its}\:{beter}\:{to}\:{use}\:{hospital}\:{theorem}…
Question Number 57408 by Abdo msup. last updated on 03/Apr/19 $${let}\:{the}\:{sequence}\:\left({a}_{{n}} \right)\:{wich}\:{verify}\:\:\:{a}_{\mathrm{1}} =\mathrm{2}\:\:{and} \\ $$$${a}_{{n}+\mathrm{1}} ={a}_{{n}} \:+\sqrt{\mathrm{1}+\frac{{a}_{{n}} }{{n}}} \\ $$$${prove}\:{that}\:\left(\frac{{a}_{{n}} }{{n}}\right)_{{n}\geqslant\mathrm{1}} \:\:\:{is}\:{convergente}. \\ $$ Terms…