Question Number 59667 by tanmay last updated on 13/May/19 Answered by tanmay last updated on 13/May/19 $$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}=\int_{{a}} ^{{b}} {f}\left({a}+{b}−{x}\right){dx} \\ $$$${I}=\int_{\mathrm{4}} ^{\mathrm{10}} \frac{\left[{x}^{\mathrm{2}}…
Question Number 125099 by bramlexs22 last updated on 08/Dec/20 $$\:{Given}\:{a}\:{function}\:{f}\left({x}\right)\:=\:\sqrt[{\mathrm{3}}]{\mathrm{2}{ax}^{\mathrm{2}} −{x}^{\mathrm{3}} }. \\ $$$${Find}\:{the}\:{inclined}\:{asymptotes} \\ $$ Answered by liberty last updated on 08/Dec/20 $$\:{k}\:=\:\underset{{x}\rightarrow\pm\infty} {\mathrm{lim}}\:\frac{{y}}{{x}}\:=\:\underset{{x}\rightarrow\pm\infty}…
Question Number 125054 by micelle last updated on 08/Dec/20 $${x}\frac{{dy}}{{dx}}−\mathrm{6}\frac{{y}}{{x}}=\mathrm{7}{x}^{\mathrm{3}} \\ $$$${help}\:{me} \\ $$ Answered by Dwaipayan Shikari last updated on 08/Dec/20 $$\frac{{dy}}{{dx}}−\frac{\mathrm{6}{y}}{{x}^{\mathrm{2}} }=\mathrm{7}{x}^{\mathrm{4}} \\…
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Question Number 190546 by cortano12 last updated on 05/Apr/23 $$\:\mathrm{Given}\:\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\:\mathrm{and}\: \\ $$$$\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} +\mathrm{x}+\mathrm{2y}+\mathrm{3z}=\mathrm{23}\: \\ $$$$\:\mathrm{find}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}+\mathrm{z}. \\ $$ Answered by mr W last updated…
Question Number 124956 by liberty last updated on 07/Dec/20 $$\:{y}\:=\:\mathrm{sec}^{−\mathrm{1}} \left({e}^{{x}^{\mathrm{4}} } \right)\:.\:{Find}\:{dy}\:=? \\ $$ Answered by bemath last updated on 07/Dec/20 $$\:\Rightarrow\:{e}^{{x}^{\mathrm{4}} } \:=\:\mathrm{sec}\:{y}\:{or}\:\mathrm{cos}\:{y}\:=\:\frac{\mathrm{1}}{{e}^{{x}^{\mathrm{4}}…
Question Number 124924 by bemath last updated on 07/Dec/20 $$\:{What}\:{should}\:{the}\:{dimensions}\:{be} \\ $$$${of}\:{a}\:{cylinder}\:{so}\:{that}\:{for}\:{a}\:{given}\:{volume}\: \\ $$$${v}\:{its}\:{total}\:{surface}\:{S}\:{minimum}\:?\: \\ $$ Commented by liberty last updated on 07/Dec/20 $${Denoting}\:{by}\:{r}\:{the}\:{radius}\:{of}\:{the}\:{base}\:{of}\:{the} \\…
Question Number 190420 by mnjuly1970 last updated on 02/Apr/23 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{laplace}\:\:\mathrm{transform} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathcal{L}_{{t}} \:\left\{\:\:\frac{\:\mathrm{sin}\left({t}\:\right)}{{t}}\:\:\right\}\:=\:\mathcal{F}\:\left({s}\:\right)\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathcal{F}\:\left({s}\:\right)=\:\:?\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:{then}\:\:{calculate}\:. \\ $$$$…
Question Number 124845 by liberty last updated on 06/Dec/20 $$\:\:\:{f}\left({x}\right)\:=\:\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)}\right)\: \\ $$$$\:\:\frac{{df}\left({x}\right)}{{dx}}\:? \\ $$ Answered by bemath last updated on 06/Dec/20 $${f}\:'\left({x}\right)=\frac{\mathrm{1}\left({x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)\right)−{x}\left(\mathrm{1}−\left(\frac{{x}−\mathrm{sin}\:{x}−{x}\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{\left({x}−\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\right)\mathrm{cos}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)\right.}{\left({x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)\right)^{\mathrm{2}} }.\:\mathrm{cos}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:\left(\frac{{x}}{{x}−\mathrm{sin}\:{x}}\right)}\right) \\…
Question Number 124831 by mnjuly1970 last updated on 06/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:\:{that}:: \\ $$$$\:\:\:{lim}_{{x}\rightarrow\infty} \left\{{xe}^{\frac{\mathrm{1}}{{x}}} −{e}^{\frac{−\mathrm{1}}{{x}}} \Gamma\left(\frac{\mathrm{1}}{{x}}\:\right)\right\}=\mathrm{2}+\gamma \\ $$$$\:\:\:\:\gamma:\:{euler}−{mascheroni}\:{constant} \\ $$$$ \\ $$ Answered by…