Question Number 200418 by mnjuly1970 last updated on 18/Nov/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{calculus}\:\:\left(\:\:\mathrm{I}\:\:\right)\:\: \\ $$$$\:\:\mathrm{I}{f}\:,\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\pi} \:\frac{\:{x}\:}{\mathrm{1}\:\:+\:\mathrm{sin}^{\mathrm{2}} \left({x}\right)}\:\mathrm{d}{x}\:=\:{a}\:\zeta\:\left(\:\mathrm{2}\:\right)\:\: \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{a}\:=\:?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:{where}\:\:,\:\:\:\zeta\:\left({s}\:\right)\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\mathrm{1}}{{n}^{\:{s}} } \\…
Question Number 200251 by Calculusboy last updated on 16/Nov/23 Answered by Mathspace last updated on 16/Nov/23 $${f}\left({x},{y}\right)={sin}\left({e}^{{xy}} +{e}^{{x}} \right)\:\Rightarrow \\ $$$$\frac{\partial}{\partial{x}}{f}\left({x},{y}\right)=\frac{\partial}{\partial{x}}\left({e}^{{xy}} +{e}^{{x}} \right){cos}\left({e}^{{xy}} +{e}^{{x}} \right)…
Question Number 199459 by cortano12 last updated on 04/Nov/23 $$\:\:\mathrm{What}\:\mathrm{minimum}\:\mathrm{value}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{z}^{\mathrm{2}} \:\mathrm{when}\: \\ $$$$\:\:\mathrm{x}+\mathrm{2y}+\mathrm{4z}=\mathrm{21} \\ $$ Answered by Frix last updated on…
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Question Number 199176 by cortano12 last updated on 29/Oct/23 $$\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)\:=\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4x}\right)\:\mathrm{sin}\:\mathrm{4x}\: \\ $$$$\:\:\:\mathrm{find}\:\mathrm{f}^{\left(\mathrm{6}\right)} \left(\mathrm{x}\right).\: \\ $$ Answered by MM42 last updated on 29/Oct/23 $${f}={u}.{v} \\…
Question Number 198953 by ArifinTanjung last updated on 26/Oct/23 $$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{3x}−\mathrm{5}}{\mathrm{2x}+\mathrm{1}}\:\rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)=….? \\ $$ Answered by Rasheed.Sindhi last updated on 26/Oct/23 $$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{3x}−\mathrm{5}}{\mathrm{2x}+\mathrm{1}}\:\rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)=….? \\ $$$$\left(\frac{{u}}{{v}}\right)^{'} =\frac{{v}\:{u}'−{u}\:{v}'}{{v}^{\mathrm{2}}…
Question Number 198988 by Safojon last updated on 26/Oct/23 Answered by witcher3 last updated on 26/Oct/23 $$\mathrm{f}\left(\mathrm{x}\right)−\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{1010}} {\sum}}\left(\mathrm{x}^{\mathrm{2k}} \right)>\mathrm{0} \\ $$$$\mathrm{u}_{\mathrm{n}} =\mathrm{f}^{\left(\mathrm{n}\right)} \left(\frac{\mathrm{1}}{\mathrm{2023}}\right),\mathrm{v}_{\mathrm{n}} =\mathrm{g}^{\left(\mathrm{n}\right)}…
Question Number 198688 by tri26112004 last updated on 23/Oct/23 $${y}''\:+\:\frac{\mathrm{2}}{{x}}.{y}'\:+\:{y}\:=\:\mathrm{0} \\ $$$${y}=¿ \\ $$ Answered by witcher3 last updated on 23/Oct/23 $$\mathrm{xy}=\mathrm{z} \\ $$$$\mathrm{xy}'+\mathrm{y}=\mathrm{z}' \\…
Question Number 198562 by cortano12 last updated on 22/Oct/23 $$\:\:\:\mathrm{f}\left(\mathrm{tan}\:\mathrm{x}\right)+\:\mathrm{2f}\left(\mathrm{cot}\:\mathrm{x}\right)\:=\:\mathrm{4x}\: \\ $$$$\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)=\:? \\ $$ Answered by dimentri last updated on 22/Oct/23 $$\:{let}\:{x}=\frac{\pi}{\mathrm{2}}−{t}\: \\ $$$$\:{f}\left(\mathrm{cot}\:{t}\right)\:+\mathrm{2}\:{f}\left(\mathrm{tan}\:{t}\right)=\:\mathrm{2}\pi−\mathrm{4}{t} \\…
Question Number 197664 by Christalin last updated on 25/Sep/23 Commented by a.lgnaoui last updated on 26/Sep/23 $$\mathrm{svp}\:\:\:\mathrm{envoyer}\:\mathrm{une}\:\mathrm{image}\:\mathrm{complete} \\ $$$$\mathrm{de}\:\mathrm{l}\:\mathrm{exercice}\:. \\ $$ Answered by a.lgnaoui last…