Question Number 20871 by j.masanja06@gmail.com last updated on 05/Sep/17 Answered by sma3l2996 last updated on 05/Sep/17 $$\frac{{dy}}{{dx}}=\mathrm{2}\frac{{tan}^{−\mathrm{1}} {x}}{\mathrm{1}+{x}^{\mathrm{2}} }\Leftrightarrow\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}=\mathrm{2}{tan}^{−\mathrm{1}} {x} \\ $$$$\frac{{d}}{{dx}}\left(\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}\right)=\mathrm{2}\frac{{d}\left({tan}^{−\mathrm{1}} {x}\right)}{{dx}}=\frac{\mathrm{2}}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 151940 by alcohol last updated on 24/Aug/21 Answered by qaz last updated on 24/Aug/21 $$\mathrm{4}\centerdot\mathrm{8}=\mathrm{32}……..\mathrm{32}\boldsymbol{\div}\mathrm{16}=\mathrm{2} \\ $$$$\mathrm{8}\centerdot\mathrm{9}=\mathrm{72}……..\mathrm{72}\boldsymbol{\div}\mathrm{24}=\mathrm{3} \\ $$$$\mathrm{9}\centerdot\mathrm{12}=\mathrm{108}…..\mathrm{108}\boldsymbol{\div}?=\mathrm{4} \\ $$$$\Rightarrow?=\mathrm{27} \\ $$…
Question Number 86407 by Power last updated on 28/Mar/20 Commented by mathmax by abdo last updated on 28/Mar/20 $$\left.{A}\:=\int\:\sqrt{\left({x}−{a}\right)\left({b}−{x}\right.}\right){dx}\:\Rightarrow{A}\:=\int\sqrt{{x}−{a}}\sqrt{{b}−{x}}{dx}\:{chsngement} \\ $$$$\sqrt{{x}−{a}}={t}\:{give}\:{x}−{a}\:={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${A}\:=\int\:\:{t}\sqrt{{b}−\left({a}+{t}^{\mathrm{2}} \right)}\left(\mathrm{2}{t}\right){dt}\:=\mathrm{2}\:\int\:{t}^{\mathrm{2}}…
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Question Number 151943 by Huy last updated on 24/Aug/21 $$\mathrm{Prove}\:\mathrm{arctan1}+\mathrm{arctan2}+\mathrm{arctan3}=\pi \\ $$ Commented by puissant last updated on 24/Aug/21 $${x}={arctan}\mathrm{1}\:,\:{y}={arctan}\mathrm{2}\:,\:{z}={arctan}\mathrm{3} \\ $$$${p}={x}+{y} \\ $$$$\Rightarrow\:{tan}\left({p}\right)={tan}\left({x}+{y}\right)=\frac{{tanx}+{tany}}{\mathrm{1}−{tanxtany}} \\…
Question Number 20869 by calculus last updated on 05/Sep/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151942 by mnjuly1970 last updated on 24/Aug/21 $$ \\ $$$$\:\:\:\mathrm{If}\:\:{x}\:,\:{y}\:>\:\mathrm{1}\:\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\:\left(\:\frac{\:{x}^{\:\mathrm{4}} }{\left({y}\:−\mathrm{1}\:\right)^{\:\mathrm{2}} }\:+\:\frac{\:{y}^{\:\mathrm{4}} }{\left(\:{x}\:−\:\mathrm{1}\:\right)^{\:\mathrm{2}} }\:\right)\:=\:?\:……\blacksquare\:\:?\:\: \\ $$$$\:\:\:\:{m}.{n}… \\ $$$$ \\…
Question Number 86405 by Power last updated on 28/Mar/20 Commented by MJS last updated on 28/Mar/20 $$\mathrm{sin}^{\mathrm{2}} \:\mathrm{3}{x}\:\mathrm{sin}^{\mathrm{3}} \:\mathrm{2}{x}\:= \\ $$$$=\frac{\mathrm{1}}{\mathrm{16}}\left(\mathrm{sin}\:\mathrm{12}{x}\:−\mathrm{3sin}\:\mathrm{8}{x}\:−\mathrm{2sin}\:\mathrm{6}{x}\:+\mathrm{3sin}\:\mathrm{4}{x}\:+\mathrm{6sin}\:\mathrm{2}{x}\right) \\ $$$$\mathrm{now}\:\mathrm{it}'\mathrm{s}\:\mathrm{super}\:\mathrm{easy} \\ $$…
Question Number 20868 by Nayon last updated on 05/Sep/17 $$\boldsymbol{{C}}×\left(\boldsymbol{{A}}+\boldsymbol{{B}}\right)=\boldsymbol{{C}}×\boldsymbol{{A}}+\boldsymbol{{C}}×\boldsymbol{{B}}\: \\ $$$${prove}\:{it}. \\ $$ Commented by Nayon last updated on 16/Sep/17 $${mr}\:{w}\mathrm{1} \\ $$ Terms…
Question Number 20867 by Tinkutara last updated on 05/Sep/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{irrational}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation} \\ $$$$\left({x}\:−\:\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{21}\:\mathrm{is} \\ $$ Answered by alex041103 last updated on 09/Sep/17 $$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left(\mathrm{3}{x}−\mathrm{2}\right)\left(\mathrm{3}{x}+\mathrm{1}\right)= \\…