Question Number 1068 by 123456 last updated on 01/Jun/15 $${f}:\mathbb{R}\rightarrow\mathbb{R}_{+} ,{g}:\mathbb{R}\rightarrow\mathbb{R}_{+} \\ $$$$\mathrm{2}{f}\left({x}\right)={f}\left({x}−\mathrm{1}\right)+{g}\left({x}+\mathrm{1}\right) \\ $$$$\left[{g}\left({x}\right)\right]^{\mathrm{2}} ={f}\left({x}−\mathrm{1}\right){g}\left({x}+\mathrm{1}\right) \\ $$$${f}\left(−\mathrm{1}\right)=\mathrm{1},{g}\left(\mathrm{1}\right)=\mathrm{2},{f}\left(\mathrm{0}\right){g}\left(\mathrm{0}\right)=? \\ $$ Answered by prakash jain last…
Question Number 1066 by 123456 last updated on 27/May/15 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{{x}}{\mathrm{tan}\:{x}}{dx} \\ $$ Answered by malwaan last updated on 01/Jun/15 $$\frac{\pi}{\mathrm{2}}{log}\left(\mathrm{2}\right) \\ $$ Terms…
Question Number 1057 by 123456 last updated on 25/May/15 $${f}:\mathbb{R}_{+} \rightarrow\mathbb{R} \\ $$$${x}={i}+{j} \\ $$$${x}\in\mathbb{R}_{+} \\ $$$${i}\in\mathbb{N} \\ $$$${j}\in\left[\mathrm{0},\mathrm{1}\right) \\ $$$${f}\left({x}\right)=\begin{cases}{{f}\left({i}−\mathrm{1}\right)+\left({i}+\mathrm{1}\right)\left({j}+\mathrm{1}\right)}&{{x}\geqslant\mathrm{1}}\\{{j}}&{\mathrm{0}\leqslant{x}<\mathrm{1}}\\{{x}}&{{x}<\mathrm{0}}\end{cases} \\ $$$${f}\left(\mathrm{9}.\mathrm{5}\right)=? \\ $$…
Question Number 132124 by Chhing last updated on 11/Feb/21 $$ \\ $$$$\:\:\:\mathrm{Calculate} \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \sqrt{\frac{\mathrm{tan}\left(\mathrm{x}\right)+\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{tan}\left(\mathrm{x}\right)−\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}\right)}}\:\mathrm{cos}\left(\mathrm{x}\right)\mathrm{dx} \\ $$$$\:\: \\ $$ Commented by liberty…
Question Number 1039 by tera last updated on 22/May/15 $${jumlah}\:{akar}−{akar}\:{persamaan}\:\left[{x}\right]^{\mathrm{2}} −\mathrm{2}\left[{x}\right]−\mathrm{3}=\mathrm{0}\:{sama}\:{dengan} \\ $$$${a}.−\mathrm{10}\:\:\:\:\:\:\:\:\:\:{b}.−\mathrm{3}\:\:\:\:\:\:{e}.\mathrm{4} \\ $$$${c}.−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:{d}.\mathrm{0} \\ $$ Commented by prakash jain last updated on 22/May/15…
Question Number 1030 by 123456 last updated on 20/May/15 $$\frac{{dy}}{{dt}}−\frac{{dx}}{{dt}}=\frac{{t}\frac{{dy}}{{dt}}+{y}}{{t}\frac{{dx}}{{dt}}+{x}} \\ $$ Answered by prakash jain last updated on 21/May/15 $${y}={k}_{\mathrm{1}} {t},{x}={k}_{\mathrm{2}} {t} \\ $$$$\frac{{dy}}{{dt}}={k}_{\mathrm{1}}…
Question Number 651 by 123456 last updated on 19/Feb/15 $$\mathrm{arg}\left(\mathrm{z}−\mathrm{a}\right)−\mathrm{arg}\left(\mathrm{z}−\mathrm{z}_{\mathrm{1}} \right)−\mathrm{arg}\left(\mathrm{z}−\bar {\mathrm{z}}_{\mathrm{1}} \right)={k}\pi \\ $$$${a}\in\mathbb{R} \\ $$$${z}_{\mathrm{1}} \in\mathbb{C},\Im\left(\bar {{z}}_{\mathrm{1}} \right)\neq\mathrm{0} \\ $$$${z}\in\mathbb{C} \\ $$$${k}\in\mathbb{Z} \\…
Question Number 66562 by Rio Michael last updated on 17/Aug/19 $${given}\:{that}\:\:\mid{z}\:−\:\mathrm{i}\mid\:=\:\mid{z}\:−\:\mathrm{4}\:+\mathrm{3}\:\mathrm{i}\mid \\ $$$${sketch}\:{the}\:{locus}\:{of}\:\:{z} \\ $$$${find}\:{the}\:{catersian}\:{equation}\:{of}\:{this}\:{locus}. \\ $$ Commented by mathmax by abdo last updated on…
Question Number 1023 by 123456 last updated on 20/May/15 $$\phi_{{n}} :\mathbb{R}\rightarrow\mathbb{R} \\ $$$${n}\in\mathbb{N}^{\ast} \\ $$$$\phi_{{n}} ={t}^{{n}} \frac{{d}^{{n}} \phi}{{dt}^{{n}} } \\ $$$$\phi_{\mathrm{1}} \left({t}\right)=?,\phi_{\mathrm{1}} \left(\mathrm{1}\right)=+\mathrm{1} \\ $$$$\phi_{\mathrm{2}}…
Question Number 66548 by AnjanDey last updated on 17/Aug/19 $$\boldsymbol{{Evaluate}}:\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}\:}{dx} \\ $$ Commented by AnjanDey last updated on 19/Aug/19 $${Please}\:{evaluate}\:{this}\:{integral}…{It}'{s}\:{very}\:{needful}\:{and}\:{urgent}… \\ $$ Terms of Service…