Question Number 205307 by universe last updated on 15/Mar/24 $$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\lfloor{a}\rfloor+\lfloor\mathrm{2}{a}\rfloor+…+\lfloor{na}\rfloor}{{n}^{\mathrm{2}} }\:\mathrm{where}\:{a}\in\mathbb{R} \\ $$$$\:\:\:\mathrm{and}\:\lfloor{x}\rfloor\:\mathrm{is}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{of}\:\mathrm{x}\:\in\:\mathbb{R} \\ $$ Commented by Frix last updated on 15/Mar/24 $$\mathrm{Just}\:\mathrm{guessing}: \\…
Question Number 205302 by cortano12 last updated on 15/Mar/24 Answered by Skabetix last updated on 15/Mar/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205297 by mnjuly1970 last updated on 15/Mar/24 $$ \\ $$$$\:\:\:{Find}\:\:{the}''\:{range}\:''\:{of}\:\:: \\ $$$$ \\ $$$$\:\:\:{i}\::\:\:\:{f}\:\left({x}\right)\:=\lfloor\:\frac{\:{x}}{\:\lfloor\:{x}\:\rfloor}\:\rfloor \\ $$$$\:\:\:{ii}:\:{f}\left({x}\right)\:=\:\frac{\:{x}}{\lfloor\:{x}\:\rfloor\:+\:\lfloor\:−{x}\:\rfloor} \\ $$$$\:\: \\ $$ Answered by A5T…
Question Number 205298 by Lindemann last updated on 15/Mar/24 $$\int\frac{{ax}+{b}}{\left({x}^{\mathrm{2}} −{cx}+{d}\right)^{{n}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205315 by cherokeesay last updated on 15/Mar/24 Answered by MM42 last updated on 16/Mar/24 $$\left[{x}\right]+\left[{x}−\frac{\mathrm{1}}{\mathrm{2}}\right]=\left[\mathrm{2}{x}\right]−\mathrm{1} \\ $$$$\Rightarrow\int_{\mathrm{0}} ^{\left[{x}\right]} \left(\left[\mathrm{2}{x}\right]−\mathrm{1}\right){dx}=\left(\left[\mathrm{2}{x}\right]−\mathrm{1}\right){x}\mid_{\mathrm{0}} ^{\left[{x}\right]} \\ $$$$=\left(\left[\mathrm{2}{x}\right]−\mathrm{1}\right)\left[{x}\right] \\…
Question Number 205279 by gopikrishnan last updated on 14/Mar/24 $$\underset{-\pi/\mathrm{2}} {\int}^{\pi/\mathrm{2}} \frac{\mathrm{8}\sqrt{\mathrm{2}}{cosx}}{\left(\mathrm{1}+\overset{{sinx}} {{e}}\right)\left(\mathrm{1}+{si}\overset{\mathrm{4}} {{n}x}\right)}{dx}={a}\pi+{blog}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\right)\:{then}\:{find}\:{a}+{b} \\ $$ Answered by Berbere last updated on 14/Mar/24 $${x}\rightarrow−{x} \\…
Question Number 205288 by mokys last updated on 14/Mar/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205289 by mr W last updated on 14/Mar/24 Answered by A5T last updated on 16/Mar/24 Commented by A5T last updated on 16/Mar/24 $${General}\:{idea},\:{there}\:{could}\:{be}\:{a}\:{far}\:{more}\:{simpler}…
Question Number 205273 by hardmath last updated on 14/Mar/24 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{2x}+\mathrm{2} \\ $$$$\mathrm{Find}\:\:\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Answered by Rasheed.Sindhi last updated on 14/Mar/24 $${Replace}\:\mathrm{x}\:{by}\:\mathrm{x}+\mathrm{1} \\ $$$$\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{2}=\mathrm{2x}+\mathrm{4} \\…
Question Number 205284 by universe last updated on 14/Mar/24 Terms of Service Privacy Policy Contact: info@tinkutara.com