Question Number 195180 by mustafazaheen last updated on 26/Jul/23 $$ \\ $$$$\mathrm{1}.\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\:,\:\:\:\:\frac{\pi}{\mathrm{2}}<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\:,\:\:\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{f}^{'} \left(\frac{\pi}{\mathrm{2}}\right)\:=? \\ $$$$\mathrm{2}.\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\:,\:\:\:\:\frac{\pi}{\mathrm{2}}<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\:,\:\:\:\:\:\mathrm{0}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{f}'\left(\mathrm{2}\pi\right)\:=? \\ $$$$ \\ $$ Answered by…
Question Number 195137 by mathlove last updated on 25/Jul/23 $${f}\left({x}\right)={arctan}\left(\frac{\mathrm{4}{sinx}}{\mathrm{3}+\mathrm{5}{cosx}}\right)\:\:\:{then}\:{f}^{'} \left(\frac{\pi}{\mathrm{3}}\right)=? \\ $$ Answered by Tokugami last updated on 02/Sep/23 $${f}'\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+\left(\frac{\mathrm{4sin}\:{x}}{\mathrm{3}+\mathrm{5cos}\:{x}}\right)^{\mathrm{2}} }\:\frac{{d}}{{dx}}\left(\frac{\mathrm{4sin}\:{x}}{\mathrm{3}+\mathrm{5cos}\:{x}}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{16sin}^{\mathrm{2}} {x}}{\left(\mathrm{3}+\mathrm{5cos}\:{x}\right)^{\mathrm{2}}…
Question Number 195170 by mathlove last updated on 25/Jul/23 $${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{7}} +\mathrm{2}{x}+\mathrm{1}\:\:\:\:\:\:\:;{x}\geqslant\mathrm{2}}\\{{x}^{\mathrm{2}} +\mathrm{7}{x}+\mathrm{4}\:\:\:\:\:\:\:\:;{x}<\mathrm{1}}\end{cases} \\ $$$${f}^{'} \left(\mathrm{1}\right)=? \\ $$ Answered by MM42 last updated on 25/Jul/23 $${f}\left(\mathrm{1}\right)\:,\:{not}\:{available}\:{so}…
Question Number 194852 by mustafazaheen last updated on 17/Jul/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cosx}\right)^{\mathrm{log}\left(\mathrm{x}\right)} =? \\ $$$$ \\ $$ Answered by MM42 last updated on 17/Jul/23…
Question Number 194467 by horsebrand11 last updated on 08/Jul/23 $$\:\:\:\underline{\downdownarrows} \\ $$ Answered by mr W last updated on 08/Jul/23 $${f}\left({x}\right)=\sqrt{\mathrm{4}^{\mathrm{2}} −\left({x}−\mathrm{4}\right)^{\mathrm{2}} }−\sqrt{\mathrm{1}^{\mathrm{2}} −\left({x}−\mathrm{7}\right)^{\mathrm{2}} }…
Question Number 194325 by horsebrand11 last updated on 03/Jul/23 $$\:\:\cancel{\mathcal{X}} \\ $$ Answered by AST last updated on 04/Jul/23 $$\sqrt[{\mathrm{4}_{} }]{\frac{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} }{\mathrm{3}}}\geqslant\sqrt{\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…
Question Number 194211 by horsebrand11 last updated on 30/Jun/23 $$\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:+\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\:\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=? \\ $$ Answered by cortano12 last updated on 30/Jun/23…
Question Number 194088 by cortano12 last updated on 27/Jun/23 Answered by horsebrand11 last updated on 27/Jun/23 $$\:\mathrm{y}^{\mathrm{2}} =\:\left(\mathrm{2}+\left(\mathrm{x}+\mathrm{x}^{\mathrm{2}} \right)\right)\left(\mathrm{1}−\left(\mathrm{x}+\mathrm{x}^{\mathrm{2}} \right)\right) \\ $$$$\:\mathrm{let}\:\mathrm{x}+\mathrm{x}^{\mathrm{2}} =\:\mathrm{u} \\ $$$$\:\mathrm{y}^{\mathrm{2}}…
Question Number 193847 by Mingma last updated on 21/Jun/23 Answered by witcher3 last updated on 21/Jun/23 $$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}−\mathrm{x}\right)}{\mathrm{x}}\mathrm{dx}=−\mathrm{Li}_{\mathrm{2}} \left(\mathrm{1}\right)=−\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}=\Sigma\mathrm{x}^{\mathrm{k}} \\ $$$$=\int_{\mathrm{0}}…
Question Number 193768 by cortano12 last updated on 19/Jun/23 $$\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{2}+\underset{\mathrm{0}} {\overset{\:\mathrm{x}} {\int}}\left(\mathrm{2t}+\mathrm{f}\left(\mathrm{t}\right)\right)^{\mathrm{2}} \mathrm{dt}\: \\ $$$$\:\:\mathrm{then}\:\underset{−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:= \\ $$ Answered by gatocomcirrose last updated on…