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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 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 $$\mathrm{Transform} \\ $$$${x}^{\mathrm{3}} −\mathrm{4}.\mathrm{375}{x}^{\mathrm{2}}…
Question Number 209872 by Frix last updated on 24/Jul/24 $$\mathrm{Solve}\:\mathrm{for}\:{x}\in\mathbb{R}: \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}=\sqrt{{x}+\mathrm{1}} \\ $$ Answered by Ghisom last updated on 24/Jul/24 $${x}={t}+\mathrm{1} \\…
Question Number 209852 by hardmath last updated on 23/Jul/24 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{arctan}\:\left(\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} }\right)\:=\:? \\ $$ Answered by mr W last updated on 24/Jul/24 $$\frac{\mathrm{2}}{{n}^{\mathrm{2}} }=\frac{\left({n}+\mathrm{1}\right)−\left({n}−\mathrm{1}\right)}{\mathrm{1}+\left({n}+\mathrm{1}\right)\left({n}−\mathrm{1}\right)}…
Question Number 209837 by lmcp1203 last updated on 23/Jul/24 $$ \\ $$$${if}\:{the}\:{series}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:{converges}\:{to}\:{k}\:.\:\:{find}\:\:{the}\:{convergence}\:{value}\:{of}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by mr W last…
Question Number 209812 by hardmath last updated on 22/Jul/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 209768 by OmoloyeMichael last updated on 20/Jul/24 $$\boldsymbol{{Express}}\:\boldsymbol{{tan}}\left(\mathrm{3}\right)\:\boldsymbol{{in}}\:\boldsymbol{{surd}}\:\boldsymbol{{form}} \\ $$ Answered by Frix last updated on 22/Jul/24 $$\mathrm{tan}\:\left(\alpha−\beta\right)\:=\frac{\mathrm{tan}\:\alpha\:−\mathrm{tan}\:\beta}{\mathrm{1}+\mathrm{tan}\:\alpha\:\mathrm{tan}\:\beta} \\ $$$$\mathrm{Use}\:\alpha=\mathrm{18}°\:\mathrm{and}\:\beta=\mathrm{15}°.\:\mathrm{The}\:\mathrm{only}\:\mathrm{problem}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{factorize}\:\mathrm{it}… \\…
Question Number 209706 by mr W last updated on 19/Jul/24 $${find}\:{the}\:{sum}\:{of}\: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+…+\mathrm{sin}^{\mathrm{2}} \:\mathrm{60}°=? \\ $$ Answered by BaliramKumar last updated on 19/Jul/24…
Question Number 209735 by hardmath last updated on 19/Jul/24 $$\mathrm{tan}\left(\mathrm{3x}\right)\:\:+\:\:\mathrm{tan}\left(\mathrm{5x}\right)\:\:=\:\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by a.lgnaoui last updated on 20/Jul/24 $$\mathrm{voir}\:\mathrm{reponse}\:\mathrm{en}\:\mathrm{bas} \\ $$$$\:\left(\mathrm{a}\:\mathrm{l}\:\mathrm{exeption}\:\:\mathrm{d}\:'\mathrm{ereur}\:\mathrm{de}\:\mathrm{calcul}\right) \\…