Question Number 217664 by hardmath last updated on 17/Mar/25 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{2x}\:+\:\mathrm{3}} \\ $$$$\mathrm{prove}\:\mathrm{that}:\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2x}\:+\:\mathrm{3}}}\: \\ $$ Answered by SdC355 last updated on 18/Mar/25 $${f}^{\left(\mathrm{1}\right)} \left({x}\right)=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({x}+{h}\right)−{f}\left({x}\right)}{{h}}. \\…
Question Number 217579 by Rasheed.Sindhi last updated on 16/Mar/25 $$\mathrm{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$$$\mathrm{Altered}\:\mathrm{Question}#\:\mathrm{217541} \\ $$ Commented by Ghisom last updated on…
Question Number 217535 by ArshadS last updated on 15/Mar/25 $$\mathrm{A}\:\mathrm{two}-\mathrm{digit}\:\mathrm{number}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{10}.\:\mathrm{When} \\ $$$$\mathrm{the}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{reversed},\:\mathrm{the}\:\mathrm{new}\:\mathrm{number} \\ $$$$\:\mathrm{is}\:\mathrm{28}\:\mathrm{less}\:\mathrm{than}\:\mathrm{twice}\:\mathrm{the}\:\:\mathrm{original}\:\mathrm{number}. \\ $$$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{original}\:\mathrm{number}. \\ $$ Answered by aleks041103 last updated…
Question Number 217541 by hardmath last updated on 15/Mar/25 $$\mathrm{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R} \\ $$$$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\:=\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{0}\right)\:=\:? \\ $$ Answered by mr W last updated on 16/Mar/25…
Question Number 217448 by ArshadS last updated on 14/Mar/25 $${Solve}\:{for}\:{x}: \\ $$$$\left(\mathrm{1}+\sqrt{\mathrm{2}}\:\right)^{{x}} +\left(\mathrm{1}−\sqrt{\mathrm{2}}\:\right)^{{x}} =\mathrm{14} \\ $$ Commented by Frix last updated on 14/Mar/25 $${a}_{{n}} =\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)^{{n}}…
Question Number 217482 by Rasheed.Sindhi last updated on 14/Mar/25 $$\left(\:{n}\sqrt{\left({n}+\mathrm{1}\right)}\:+\left({n}+\mathrm{1}\right)\sqrt{{n}}\:\:\right)^{{n}} +\left(\:{n}\sqrt{\left({n}+\mathrm{1}\right)}\:−\left({n}+\mathrm{1}\right)\sqrt{{n}}\:\:\right)^{{n}} ={n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{3}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 217424 by peter frank last updated on 13/Mar/25 The angle of elevation of the top of a building 24 m high is observed…
Question Number 217416 by peter frank last updated on 13/Mar/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 217417 by peter frank last updated on 13/Mar/25 Commented by mr W last updated on 13/Mar/25 $${for}\:{f}\left({g}\left({x}\right)\right)=\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{50}} \:{there}\:{is}\:{no} \\ $$$${unique}\:{solution}\:{for}\:{f}\left({x}\right)\:{and}\:{f}\left({x}\right). \\ $$…
Question Number 217389 by Simurdiera last updated on 12/Mar/25 $$\mathrm{Resolver} \\ $$$$\frac{\mid{x}\:−\:\mathrm{1}\mid\:+\:\mid{x}\:+\:\mathrm{2}\mid}{\mid{x}\mid\:−\:\mathrm{1}}\:\leq\:\mathrm{3} \\ $$ Answered by A5T last updated on 13/Mar/25 $$\mathrm{when}\:−\mathrm{2}\leqslant\mathrm{x}<−\mathrm{1};\:\mid\mathrm{x}−\mathrm{1}\mid=\mathrm{1}−\mathrm{x},\:\mid\mathrm{x}+\mathrm{2}\mid=\mathrm{x}+\mathrm{2}\wedge\:\mid\mathrm{x}\mid=−\mathrm{x} \\ $$$$\Rightarrow\frac{\mid\mathrm{x}−\mathrm{1}\mid+\mid\mathrm{x}+\mathrm{2}\mid}{\mid\mathrm{x}\mid−\mathrm{1}}\leqslant\mathrm{3}\Rightarrow\frac{\mathrm{1}−\mathrm{x}+\mathrm{x}+\mathrm{2}}{−\mathrm{x}−\mathrm{1}}\leqslant\mathrm{3} \\…