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 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 $${Replace}\:\mathrm{x}\:{by}\:\mathrm{x}+\mathrm{1} \\ $$$$\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{2}=\mathrm{2x}+\mathrm{4} \\…
Question Number 205211 by cortano12 last updated on 13/Mar/24 Answered by Berbere last updated on 13/Mar/24 $$\begin{cases}{\mathrm{5}{x}^{\mathrm{2}} \left({y}^{\mathrm{2}} −\mathrm{1}\right)=\mathrm{4}{x}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}\\{\mathrm{5}{y}^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{3}{y}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)}\end{cases}…
Question Number 205238 by necx122 last updated on 13/Mar/24 $$\mathrm{4}^{{x}} \:+\:{x}\:=\:\mathrm{260} \\ $$$${find}\:{the}\:{possible}\:{values}\:{of}\:{x} \\ $$$$ \\ $$ Commented by Ghisom last updated on 13/Mar/24 $$\mathrm{generally}…
Question Number 205256 by hardmath last updated on 13/Mar/24 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:? \\ $$ Commented by mr W last updated on 13/Mar/24 $${your}\:{earnest}? \\ $$ Commented…
Question Number 205220 by hardmath last updated on 13/Mar/24 $$\mathrm{cos}^{\mathrm{4}} \:\mathrm{x}\:−\:\mathrm{sin}^{\mathrm{4}} \:\mathrm{x}\:=\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{x} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by Sutrisno last updated on 13/Mar/24 $$\left({cos}^{\mathrm{2}}…
Question Number 205218 by hardmath last updated on 13/Mar/24 $$\mid\:\mathrm{sinx}\mid\:+\:\mid\:\mathrm{cosx}\:\mid\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by Sutrisno last updated on 13/Mar/24 $$ \\ $$$$\left(\mid\:\mathrm{sinx}\mid\:+\:\mid\:\mathrm{cosx}\:\mid\:\right)^{\mathrm{2}} =\:\mathrm{1}^{\mathrm{2}}…
Question Number 205217 by hardmath last updated on 13/Mar/24 $$\mathrm{4}\:\mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by A5T last updated on 13/Mar/24 $$\mathrm{2}{sinx}=\mathrm{2}{sin}\left(\frac{{x}}{\mathrm{2}}+\frac{{x}}{\mathrm{2}}\right)=\mathrm{4}{sin}\left(\frac{{x}}{\mathrm{2}}\right){cos}\left(\frac{{x}}{\mathrm{2}}\right)=\mathrm{1} \\ $$$$\Rightarrow{sinx}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}=\mathrm{30}°+\mathrm{360}{n};\mathrm{150}°+\mathrm{360}{n} \\…
Question Number 205219 by hardmath last updated on 13/Mar/24 $$\begin{cases}{\mathrm{sinx}\:+\:\mathrm{cosx}\:=\:\mathrm{1}}\\{\mathrm{sinx}\:−\:\mathrm{cosy}\:=\:\mathrm{1}}\end{cases} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 13/Mar/24 $$\begin{cases}{\mathrm{sinx}\:+\:\mathrm{cosx}\:=\:\mathrm{1}…{i}}\\{\mathrm{sinx}\:−\:\mathrm{cosy}\:=\:\mathrm{1}…{ii}}\end{cases}\:\:\:;\mathrm{x}\:=\:? \\ $$$$\mathrm{cos}\:{x}+\mathrm{cos}\:{y}=\mathrm{0} \\…
Question Number 205173 by mr W last updated on 12/Mar/24 $${find} \\ $$$${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({a}^{\mathrm{2}} +{n}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$ Commented by lepuissantcedricjunior last updated…