Question Number 22946 by ANTARES_VY last updated on 24/Oct/17 $$\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{1}}{\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}−\mathrm{2}}\boldsymbol{\mathrm{dx}}\:\:\:?\boldsymbol{\mathrm{solve}} \\ $$ Answered by ajfour last updated on 24/Oct/17 $$=\mathrm{ln}\:\mathrm{19}\: \\ $$…
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Question Number 88461 by otchereabdullai@gmail.com last updated on 10/Apr/20 Commented by mr W last updated on 10/Apr/20 $${x}=\mathrm{20}° \\ $$$${see}\:{Q}\mathrm{61347} \\ $$ Commented by otchereabdullai@gmail.com…
Question Number 153993 by ZiYangLee last updated on 12/Sep/21 $$\mathrm{Given}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\mathrm{12}} {f}\left({x}\right)\:{dx}=\mathrm{20}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{1}} ^{\:\mathrm{8}} \:\frac{{f}\left(\mathrm{4}\:\mathrm{log}_{\mathrm{2}} {x}\right)}{{x}}\:{dx}. \\ $$ Answered by mr W last updated…
Question Number 153973 by liberty last updated on 12/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 12/Sep/21 $${A}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}=\frac{\mathrm{1}}{\mathrm{3}}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}+\frac{\mathrm{1}}{\mathrm{3}}}−\frac{\mathrm{1}}{{n}+\frac{\mathrm{2}}{\mathrm{3}}}\right) \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{3}}\left(\psi\left(\frac{\mathrm{2}}{\mathrm{3}}\right)−\psi\left(\frac{\mathrm{1}}{\mathrm{3}}\right)\right)=\frac{\pi}{\mathrm{3}}\mathrm{cot}\left(\frac{\pi}{\mathrm{3}}\right)=\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{9}} \\ $$…
Question Number 88439 by otchereabdullai@gmail.com last updated on 10/Apr/20 $$\mathrm{kofi}\:\mathrm{have}\:\mathrm{three}\:\mathrm{books}\:\mathrm{on}\:\mathrm{his}\:\mathrm{desk},\:\mathrm{they} \\ $$$$\mathrm{are}\:\mathrm{mathematics}\:,\:\mathrm{biology}\:\mathrm{and}\:\mathrm{physics}. \\ $$$$\mathrm{Ama}\:\mathrm{also}\:\mathrm{have}\:\mathrm{three}\:\mathrm{books}\:\mathrm{on}\: \\ $$$$\mathrm{her}\:\mathrm{desk}\:\mathrm{namely}\:\mathrm{physics}\:,\mathrm{mathematics} \\ $$$$\mathrm{and}\:\mathrm{chemistry}.\:\mathrm{A}\:\mathrm{thief}\:\mathrm{picked}\:\mathrm{one}\:\mathrm{book} \\ $$$$\mathrm{from}\:\mathrm{each}\:\mathrm{of}\:\mathrm{their}\:\mathrm{desk}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{of}\:\mathrm{picking}\:\mathrm{mathematics}\: \\ $$$$\mathrm{book} \\…
Question Number 153972 by SANOGO last updated on 12/Sep/21 $${soit}:{f}\rightarrow{x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{1} \\ $$$${alors}:\left({f}^{\_\mathrm{1}} \right)^{''} \left(\mathrm{5}\right)=? \\ $$ Answered by mr W last updated on 12/Sep/21…
Question Number 153965 by ZiYangLee last updated on 12/Sep/21 $$\mathrm{If}\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{xy}+{y}^{\mathrm{2}} =\mathrm{1},\:\mathrm{prove}\:\mathrm{that}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{\mathrm{2}}{\left({x}−{y}\right)^{\mathrm{3}} } \\ $$ Answered by ARUNG_Brandon_MBU last updated on 12/Sep/21 $$\mathrm{3}{x}^{\mathrm{2}}…
Question Number 22893 by NECx last updated on 23/Oct/17 $${A}\:{wedge}\:{has}\:{two}\:{equally}\:{rough} \\ $$$${faces}\:{each}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the} \\ $$$${horizontal}.{Masses}\:{of}\:\mathrm{5}{kg}\:{and}\:\mathrm{2}{kg} \\ $$$$,{one}\:{on}\:{each}\:{face},{are}\:{connected} \\ $$$${by}\:{a}\:{light}\:{string}\:{passing}\:{over}\:{a} \\ $$$${smooth}\:{pulley}\:{at}\:{the}\:{top}\:{of}\:{the} \\ $$$${wedge}.{The}\:{coefficient}\:{of}\:{friction}\: \\ $$$$\mu,\:{between}\:{each}\:{masses}\:{and}\:{the} \\…
Question Number 153963 by ZiYangLee last updated on 12/Sep/21 $$\mathrm{Given}\:\mathrm{that}\:{f}\:\mathrm{and}\:{g}\:\mathrm{are}\:\mathrm{differentiable} \\ $$$$\mathrm{functions}\:\mathrm{such}\:\mathrm{that}\:{f}\:'\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\left({f}\left({x}\right)\right)^{\mathrm{2}} }\:}, \\ $$$$\mathrm{and}\:{g}={f}^{\:−\mathrm{1}} \:,\:\mathrm{find}\:{g}'\left({x}\right). \\ $$ Answered by mr W last updated on…