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) \\…
Question Number 159664 by mnjuly1970 last updated on 19/Nov/21 $$ \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\Phi\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{4}} \left({x}\right)}{{x}^{\:\mathrm{3}} }{dx}=\:\:{ln}\left(\mathrm{2}\right) \\ $$$$\:\:\:−−−−−−−−− \\ $$$$ \\…
Question Number 94125 by i jagooll last updated on 17/May/20 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{function}\: \\ $$$$\mathrm{H}\left(\mathrm{x}\right)\:=\:\mid\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\mid\:+\:\sqrt{\mathrm{2}}\:\mathrm{cos}\:\mathrm{x} \\ $$$$\mathrm{with}\:\mathrm{x}\:\in\:\left[\:\mathrm{0},\:\mathrm{2}\pi\:\right]\: \\ $$$$\mathrm{find}\:\mathrm{H}\left(\mathrm{x}\right)_{\mathrm{max}} \:\mathrm{and}\:\mathrm{H}\left(\mathrm{x}\right)_{\mathrm{min}} \\ $$ Answered by john santu last…
Question Number 94110 by Jidda28 last updated on 16/May/20 Commented by mathmax by abdo last updated on 17/May/20 $$\left.{a}\right)\:{let}\:{take}\:{a}\:{try}\:{let}\:{f}\left({x}\right)\:={e}^{{cosx}} \:\:\:\:{maclaurin}\:{at}\:\mathrm{0} \\ $$$${f}\left({x}\right)\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{f}^{\left({n}\right)} \left(\mathrm{0}\right)}{{n}!}{x}^{{n}}…