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Find-0-x-x-x-1-dx-x-fractional-part-x-full-part-

Question Number 209918 by hardmath last updated on 25/Jul/24 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left\{\mathrm{x}\right\}^{\left[\boldsymbol{\mathrm{x}}\right]} }{\left[\mathrm{x}\right]\:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$$$\left\{\mathrm{x}\right\}\:\rightarrow\:\mathrm{fractional}\:\mathrm{part} \\ $$$$\left[\mathrm{x}\right]\:\:\:\rightarrow\:\mathrm{full}\:\mathrm{part} \\ $$ Answered by MM42 last updated on…

Question-209911

Question Number 209911 by 073 last updated on 25/Jul/24 Commented by mr W last updated on 25/Jul/24 $${what}'{s}\:{the}\:{difference}\:{between} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\right)^{\mathrm{2}} \:{and}\:\left(\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\right)^{\mathrm{2}} \right)? \\ $$ Commented…

Question-209880

Question Number 209880 by mnjuly1970 last updated on 24/Jul/24 Answered by mahdipoor last updated on 25/Jul/24 $${get}\::\:\:\:{a}={cte}\:\:{and}\:\:\:{A},{B},{C}\:\:{is}\:{variable} \\ $$$${f}\left({A},{B},{C}\right)=\frac{\sqrt{{cosA}}}{{a}}+\frac{\sqrt{{cosB}}}{{b}}+\frac{\sqrt{{cosC}}}{{c}}= \\ $$$$\frac{\mathrm{1}}{{a}}\left(\sqrt{{cosA}}+{sinA}\left(\frac{\sqrt{{cosB}}}{{sinB}}+\frac{\sqrt{{cosC}}}{{sinC}}\right)\right) \\ $$$${g}\left({A},{B},{C}\right)={A}+{B}+{C}=\mathrm{180} \\ $$$$\Rightarrow\frac{\partial{f}}{\partial{x}_{{i}}…

Let-n-be-positive-integer-satisfies-a-n-1-1-n-1-n-1-1-n-1-n-1-Find-the-value-of-a-1-a-2-a-3-a-99-

Question Number 209881 by naka3546 last updated on 24/Jul/24 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{satisfies} \\ $$$$ \\ $$$${a}_{{n}} \:=\:\mathrm{1}\:+\:\sqrt{\frac{\mathrm{1}}{{n}}}\:−\:\sqrt{\frac{\mathrm{1}}{{n}+\mathrm{1}}}\:−\:\sqrt{\frac{\mathrm{1}}{{n}}\:−\:\frac{\mathrm{1}}{{n}+\mathrm{1}}} \\ $$$$ \\ $$$$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{value}\:\:\mathrm{of}\: \\ $$$$ \\ $$$$\:\:\:{a}_{\mathrm{1}} {a}_{\mathrm{2}} {a}_{\mathrm{3}}…

1-6-2x-2-3-2x-2-2-x-find-x-

Question Number 209876 by hardmath last updated on 24/Jul/24 $$\mathrm{1},\mathrm{6}\:\:=\:\:\frac{\left(\mathrm{2x}\right)^{\mathrm{2}} }{\left(\mathrm{3}−\mathrm{2x}\right)^{\mathrm{2}} \:\centerdot\:\left(\mathrm{2}−\mathrm{x}\right)}\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Frix last updated on 24/Jul/24 $$\mathrm{Transform} \\ $$$${x}^{\mathrm{3}} −\mathrm{4}.\mathrm{375}{x}^{\mathrm{2}}…