Question Number 159982 by ArielVyny last updated on 23/Nov/21 $$\left(\mathrm{1}+{bf}\left({x}\right)\right){f}''\left({x}\right)=\frac{{p}}{\lambda{a}} \\ $$$${solve}\:{this}\:{equation}:\:{find}\:\:{f}\left({x}\right) \\ $$ Answered by mr W last updated on 23/Nov/21 $${let}\:{y}'={u} \\ $$$${y}''=\frac{{du}}{{dx}}=\frac{{du}}{{dy}}×\frac{{dy}}{{dx}}={u}\frac{{du}}{{dy}}…
Question Number 28903 by amit96 last updated on 01/Feb/18 Commented by abdo imad last updated on 01/Feb/18 $${let}\:{put}\:{I}=\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\left[\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right]{dx}\:\:\:{and}\:{use}\:{the}\:{ch}.\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }={t}\:\Leftrightarrow{x}^{\mathrm{2}} =\frac{\mathrm{1}}{{t}} \\ $$$$\Leftrightarrow{x}=\frac{\mathrm{1}}{\:\sqrt{{t}}}\:\Rightarrow\:{dx}=\frac{−\mathrm{1}}{\mathrm{2}{t}\sqrt{{t}}}{dt}\:\:\:{and}\:\:{I}=\:−\int_{\mathrm{1}}…
Question Number 28894 by amit96 last updated on 01/Feb/18 Commented by abdo imad last updated on 01/Feb/18 $${let}\:{put}\:{f}\left({x}\right)={F}\left({x},{y}\right)=\:\int_{\mathrm{0}} ^{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } {cos}^{\mathrm{2}} \left({t}+{x}\right){dt}\:\:{we}\:{have}\:{by}\:{ch}. \\ $$$${t}+{x}={u}\:\:\:\:\Rightarrow{f}\left({x}\right)=\:\int_{{x}}…
Question Number 159966 by malwaan last updated on 23/Nov/21 $${a}\:\:\:\:{y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+…..}}} \\ $$$${b}\:\:\:\:\:{y}=\sqrt{{x}\sqrt{{x}\sqrt{{x}\sqrt{{x}…..}}}} \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$ Commented by tounghoungko last updated on 23/Nov/21 $$\left({a}\right){y}=\sqrt{{x}+{y}} \\…
Question Number 159918 by tounghoungko last updated on 22/Nov/21 $$\:\:{y}\:=\:\mathrm{sin}\:\mathrm{8}{x}\:\mathrm{cos}\:\mathrm{4}{x}\: \\ $$$$\:\:{y}^{\left({n}\right)} \:=? \\ $$ Commented by blackmamba last updated on 22/Nov/21 $$\:\:\:{y}=\:\mathrm{sin}\:\mathrm{8}{x}\:\mathrm{cos}\:\mathrm{4}{x}\:\Rightarrow{y}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{sin}\:\mathrm{12}{x}+\mathrm{sin}\:\mathrm{4}{x}\right) \\ $$$$\:\:\:{y}\:'=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{12cos}\:\mathrm{12}{x}+\mathrm{4cos}\:\mathrm{4}{x}\right)…
Question Number 159874 by tounghoungko last updated on 22/Nov/21 $$\:\:\:\:{Given}\:{the}\:{curve}\:{y}={x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{3}} −\mathrm{6}{x}^{\mathrm{2}} −\mathrm{3}{x} \\ $$$$\:{determine}\:{for}\:{which}\:{value}\: \\ $$$$\:{of}\:\alpha\:{the}\:{tangent}\:{to}\:{the}\:{curve} \\ $$$$\:{from}\:{point}\:{P}\left(\alpha,\mathrm{0}\right)\:{is}\:{maximum}. \\ $$ Commented by mr W…
Question Number 159854 by mnjuly1970 last updated on 21/Nov/21 $$ \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} {x}.{ln}\left({sin}\left({x}\right)\right){dx}=\:? \\ $$$$ \\ $$$$ \\ $$ Answered by mindispower…
Question Number 94245 by mhmd last updated on 17/May/20 $${find}\:{the}\:{function}\:{f}\left({x}\right)\:{satisfying}\:{the}\:{given}\:{conditions} \\ $$$$\left({i}\right){f}^{'} \left({x}\right)=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}\:\:\:,\:{f}\left(\mathrm{0}\right)=\mathrm{3}\:? \\ $$$$\left({ii}\right){f}^{''} \left({x}\right)=\mathrm{12}\:\:,\:{f}^{'} \left(\mathrm{0}\right)=\mathrm{2}\:\:,\:{f}\left(\mathrm{0}\right)=\mathrm{3}\:? \\ $$$$\left({iii}\right){f}^{''} \left({x}\right)=\mathrm{2}{x}\:\:,\:\:{f}^{'} \left(\mathrm{0}\right)=−\mathrm{3}\:\:,\:{f}\left(\mathrm{0}\right)=\mathrm{2}\:? \\ $$$$ \\…
Question Number 94210 by Pars1z last updated on 17/May/20 $$\frac{{s}\left({t}+\Delta{t}\right)−{s}\left({t}\right)}{\Delta{t}} \\ $$ Answered by prakash jain last updated on 17/May/20 $$\underset{\Delta{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{s}\left({t}+\Delta{t}\right)−{s}\left({t}\right)}{\Delta{t}}=\frac{{ds}}{{dt}}={v} \\ $$$$\mathrm{where}\:{s}\:\mathrm{is}\:\mathrm{distance} \\…
Question Number 159719 by tounghoungko last updated on 20/Nov/21 $$\:\:\:\:\:{F}\left({x}\right)=\:\mathrm{3cos}\:{x}\:+\:\mathrm{4sin}\:{x}\:,\:{F}^{\left(\mathrm{101}\right)} \left(\frac{\pi}{\mathrm{2}}\right)=? \\ $$ Answered by mathmax by abdo last updated on 20/Nov/21 $$\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)=\mathrm{3cos}\left(\mathrm{x}+\frac{\mathrm{n}\pi}{\mathrm{2}}\right)+\mathrm{4sin}\left(\mathrm{x}+\frac{\mathrm{n}\pi}{\mathrm{2}}\right) \\…