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Category: Differentiation

Question-20903

Question Number 20903 by ANTARES_VY last updated on 07/Sep/17 Answered by Joel577 last updated on 07/Sep/17 $$\mathrm{Using}\:\mathrm{polynomial}\:\mathrm{division},\mathrm{we}\:\mathrm{got} \\ $$$${I}\:=\:\int\:{x}^{\mathrm{3}} \:−\:{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}\:−\:\mathrm{4}\:+\:\frac{\mathrm{4}{x}\:+\:\mathrm{1}}{{x}^{\mathrm{2}} \:+\:{x}}\:{dx} \\ $$$$\:\:\:=\:\int\:{x}^{\mathrm{3}} \:−\:{x}^{\mathrm{2}}…

Question-151940

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-20871

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}}…

If-x-y-gt-1-Min-x-4-y-1-2-y-4-x-1-2-m-n-

Question Number 151942 by mnjuly1970 last updated on 24/Aug/21 $$ \\ $$$$\:\:\:\mathrm{If}\:\:{x}\:,\:{y}\:>\:\mathrm{1}\:\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\:\left(\:\frac{\:{x}^{\:\mathrm{4}} }{\left({y}\:−\mathrm{1}\:\right)^{\:\mathrm{2}} }\:+\:\frac{\:{y}^{\:\mathrm{4}} }{\left(\:{x}\:−\:\mathrm{1}\:\right)^{\:\mathrm{2}} }\:\right)\:=\:?\:……\blacksquare\:\:?\:\: \\ $$$$\:\:\:\:{m}.{n}… \\ $$$$ \\…