Question Number 83085 by mathmax by abdo last updated on 27/Feb/20 $$\left.\mathrm{1}\right)\:{find}\:\int\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{4}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{4}} } \\ $$ Commented by abdomathmax…
Question Number 148609 by learner001 last updated on 29/Jul/21 $$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{a}_{\mathrm{n}} \right)_{\mathrm{n}\geqslant\mathrm{1}\:} \mathrm{defined}\:\mathrm{by}\:\mathrm{a}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{6}}+…+\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)}\:\mathrm{is}\: \\ $$$$\mathrm{cauchy}\:\mathrm{sequence}. \\ $$ Commented by learner001 last updated on 29/Jul/21 $$\mathrm{This}\:\mathrm{is}\:\mathrm{what}\:\mathrm{i}\:\mathrm{tried}.…
Question Number 83074 by ~blr237~ last updated on 27/Feb/20 $${find}\:{all}\:{function}\:\:{satisfying}\:\:\forall\:{x}\in\mathbb{R}\backslash\left\{{k}\pi\:,\:\:{k}\in\mathbb{Z}\right\} \\ $$$${f}\left({x}\right)+\int_{\mathrm{0}} ^{\mathrm{1}} {f}^{\mathrm{2}} \left({x}\right){dx}=\frac{{x}}{{sin}\left(\pi{x}\right)} \\ $$ Commented by mr W last updated on 28/Feb/20…
Question Number 148600 by EDWIN88 last updated on 29/Jul/21 $$\:\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{27}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} }\:+\sqrt[{\mathrm{3}}]{\mathrm{8}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} }−\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} +\mathrm{2021}}\:=?\: \\ $$ Answered by bemath last updated on…
Question Number 17530 by Tinkutara last updated on 07/Jul/17 $$\mathrm{Two}\:\mathrm{masses}\:\mathrm{5}\:\mathrm{kg}\:\mathrm{and}\:{M}\:\mathrm{are}\:\mathrm{hanging} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{light}\:\mathrm{rope}\:\mathrm{and}\:\mathrm{pulley} \\ $$$$\mathrm{as}\:\mathrm{shown}\:\mathrm{below}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\:\mathrm{in} \\ $$$$\mathrm{equilibrium}\:\mathrm{then}\:{M}\:= \\ $$ Commented by Tinkutara last updated on 07/Jul/17…
Question Number 83064 by M±th+et£s last updated on 27/Feb/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{sin}\left({nx}\right)}{{sin}\left({x}\right)}{dx}=\frac{\pi}{\mathrm{2}} \\ $$$${n}\:{is}\:{posative}\:{odd}\:{number} \\ $$ Answered by mind is power last updated…
Question Number 83063 by M±th+et£s last updated on 27/Feb/20 Commented by M±th+et£s last updated on 27/Feb/20 $${thank}\:{you}\:{sir} \\ $$ Commented by abdomathmax last updated on…
Question Number 148599 by mathdanisur last updated on 29/Jul/21 $${f}\::\:\mathbb{Z}\:\rightarrow\:\mathbb{Z} \\ $$$${f}\left({x}\right)\:=\:\mathrm{2}\:\centerdot\:{f}\left({x}\:-\:\mathrm{1}\right) \\ $$$${f}\left(\mathrm{5}\right)\:=\:\mathrm{4} \\ $$$${find}\:\:\:{f}\left(\mathrm{30}\right)\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 29/Jul/21…
Question Number 17525 by alex041103 last updated on 07/Jul/17 $$\mathrm{Evaluate}\:\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\frac{{n}}{\mathrm{2}}} {dx}\:\:\mathrm{for}\: \\ $$$${n}\:\in\:\mathbb{Z}\cap\left[\mathrm{0};\infty\right)\:\left(\mathrm{i}.\mathrm{e}.\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:…\right)\:\mathrm{and}: \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\:\:{n}\:\equiv\:\mathrm{0}\left({mod}\:\mathrm{2}\right) \\ $$$$\left.\boldsymbol{{b}}\right)\:{n}\:\equiv\:\mathrm{1}\left({mod}\:\mathrm{2}\right) \\ $$ Commented by alex041103…
Question Number 17524 by 786 last updated on 07/Jul/17 $$\mathrm{The}\:\mathrm{circle}\:\omega\:\mathrm{touches}\:\mathrm{the}\:\mathrm{circle}\:\Omega \\ $$$$\mathrm{internally}\:\mathrm{at}\:{P}.\:\mathrm{The}\:\mathrm{centre}\:{O}\:\mathrm{of}\:\Omega\:\mathrm{is} \\ $$$$\mathrm{outside}\:\omega.\:\mathrm{Let}\:{XY}\:\mathrm{be}\:\mathrm{a}\:\mathrm{diameter}\:\mathrm{of}\:\Omega \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{also}\:\mathrm{tangent}\:\mathrm{to}\:\omega.\:\mathrm{Assume} \\ $$$${PY}\:>\:{PX}.\:\mathrm{Let}\:{PY}\:\mathrm{intersect}\:\omega\:\mathrm{at}\:{Z}.\:\mathrm{If} \\ $$$${YZ}\:=\:\mathrm{2}{PZ},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of} \\ $$$$\angle{PYX}\:\mathrm{in}\:\mathrm{degrees}? \\ $$ Answered…