Question Number 134058 by john_santu last updated on 27/Feb/21 $$\mathcal{J}\:=\:\int\:\frac{{dx}}{\mathrm{1}+\mathrm{tan}\:{x}+\mathrm{csc}\:{x}+\mathrm{cot}\:{x}+\mathrm{sec}\:{x}} \\ $$ Answered by john_santu last updated on 27/Feb/21 $$\mathcal{J}=\int\:\frac{{dx}}{\mathrm{1}+\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}} \\ $$$$\:=\:\int\:\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\mathrm{cos}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}} \\…
Question Number 68521 by naka3546 last updated on 13/Sep/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{4}\:\mathrm{sin}\:{x}\:+\:\mathrm{2}\:\mathrm{tan}\:{x}\:−\:\mathrm{6}{x}}{{x}^{\mathrm{5}} }\:\:=\:\:? \\ $$$${Without}\:\:{L}'{Hospital} \\ $$ Commented by mathmax by abdo last updated on 13/Sep/19…
Question Number 2983 by Syaka last updated on 02/Dec/15 $$\underset{\mathrm{2}} {\overset{{m}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\underset{{n}\:\rightarrow\:\infty} {{lim}}\:\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\left(\mathrm{1}\:+\frac{{k}}{{n}}\right)\left(\frac{\mathrm{2}{k}}{{n}}\right) \\ $$$$ \\ $$$${m}\:+\:{f}\left({m}\right)\:=\:? \\ $$ Commented by prakash jain…
Question Number 134052 by shaker last updated on 27/Feb/21 Answered by mathmax by abdo last updated on 27/Feb/21 $$\mathrm{I}\:=\int\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\mathrm{3}}\mathrm{dx}\:\:\Rightarrow\mathrm{I}\:=\int\:\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\left(\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{6}}} \right)^{\mathrm{6}} }\mathrm{dx}\:=_{\mathrm{x}=\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{6}}}…
Question Number 68517 by A8;15: last updated on 12/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2980 by Filup last updated on 02/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\frac{{d}}{{dx}}\left({e}^{{x}} \right)={e}^{{x}} \\ $$$$\mathrm{Assume}\:\mathrm{that}\:\mathrm{you}\:\mathrm{do}\:\mathrm{not}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{above}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{true}. \\ $$ Answered by RasheedAhmad last updated on 02/Dec/15 $${e}^{{x}}…
Question Number 134049 by benjo_mathlover last updated on 27/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 2979 by Filup last updated on 02/Dec/15 $$\mathrm{If}\:\mathrm{a}\:\mathrm{parabola}\:\mathrm{is}\:\mathrm{in}\:\mathrm{form}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c}, \\ $$$$\mathrm{why}\:\mathrm{is}\:{g}\left({x}\right)={e}^{{x}} +{e}^{−{x}} \:\:\mathrm{parabolic}? \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{it}\:\mathrm{have}\:\mathrm{to}\:\mathrm{do}\:\mathrm{with}\:\mathrm{its}\:\mathrm{locus}? \\ $$ Commented by 123456 last…
Question Number 68515 by azizullah last updated on 12/Sep/19 Commented by Prithwish sen last updated on 13/Sep/19 $$\left[\mathrm{z}\left(\mathrm{z}−\mathrm{6}\right)\right]^{\mathrm{2}} =\left[\left(\mathrm{3}+\mathrm{2i}\right)\left(\mathrm{3}+\mathrm{2i}−\mathrm{6}\right)\right]^{\mathrm{2}} =\left[\left(\mathrm{2i}\right)^{\mathrm{2}} −\left(\mathrm{3}\right)^{\mathrm{2}} \right]^{\mathrm{2}} \\ $$$$=\left(−\mathrm{13}\right)^{\mathrm{2}} =\mathrm{169}…
Question Number 68510 by oyemi kemewari last updated on 12/Sep/19 Answered by mr W last updated on 14/Sep/19 $${v}=\sqrt{\mathrm{2}{gh}} \\ $$$${base}\:{area}\:{of}\:{tanks}={A}=\mathrm{1}\:{ft}^{\mathrm{2}} \\ $$$${A}\frac{{dh}}{\mathrm{2}}=−\frac{\pi{d}^{\mathrm{2}} }{\mathrm{4}}{vdt} \\…