Question Number 2300 by Syaka last updated on 14/Nov/15 $${if}\:{f}\left(\mathrm{4}{xy}\right)\:=\:\mathrm{2}{y}\left({f}\left({x}\:−\:{y}\right)\:+\:{f}\left({x}\:+\:{y}\right)\right)\:{and}\:{f}\left(\mathrm{5}\right)\:=\:\mathrm{3} \\ $$$${what}\:{is}\:{the}\:{value}\:{of}\:{f}\left(\mathrm{2015}\right)\:=\:? \\ $$ Commented by Rasheed Soomro last updated on 17/Nov/15 $$\mathcal{EXCELLENT}\:! \\ $$…
Question Number 133368 by otchereabdullai@gmail.com last updated on 21/Feb/21 $$\mathrm{Assuming}\:\mathrm{that}\:\mathrm{the}\:\mathrm{world}\:\mathrm{population} \\ $$$$\mathrm{is}\:\mathrm{6billion}\:\mathrm{and}\:\mathrm{total}\:\mathrm{world}\:\mathrm{trip}\:\mathrm{is} \\ $$$$\mathrm{4}.\mathrm{8billion}. \\ $$$$\left(\mathrm{a}\right)\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{country}\:\mathrm{potential}\: \\ $$$$\mathrm{generation}\:\mathrm{index}\:\left(\mathrm{CPGI}\right)\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{country} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{interprete}\:\mathrm{your}\:\mathrm{results}\:\mathrm{in}\:\left(\mathrm{a}\right)\:\mathrm{above}. \\ $$$$ \\…
Question Number 2292 by Filup last updated on 14/Nov/15 $$\mathrm{This}\:\mathrm{isn}'\mathrm{t}\:\mathrm{a}\:\mathrm{question}. \\ $$$$\mathrm{Just}\:\mathrm{wanted}\:\mathrm{to}\:\mathrm{say}\:\mathrm{that}\:\mathrm{since}\:\mathrm{I}\:\mathrm{joined} \\ $$$$\mathrm{here}\:\mathrm{I}\:\mathrm{have}\:\mathrm{learnt}\:\mathrm{so}\:\mathrm{much}.\:\mathrm{You}\:\mathrm{guys} \\ $$$$\mathrm{are}\:\mathrm{awesome}! \\ $$ Answered by Rasheed Soomro last updated on…
Question Number 2286 by Filup last updated on 14/Nov/15 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{evaluate}: \\ $$$$\frac{\mathrm{1}}{\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}}}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}}}}+…+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{…}} \\ $$ Commented by Yozzi last updated on 14/Nov/15 $${u}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{1}},\:{u}_{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}}}=\frac{\mathrm{1}}{\mathrm{1}+{u}_{\mathrm{1}} }…
Question Number 133341 by mohammad17 last updated on 21/Feb/21 Answered by mathmax by abdo last updated on 21/Feb/21 $$\left.\mathrm{1}\right)\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:+\mathrm{4x}^{\mathrm{2}} −\mathrm{10}\:\:\:\:\Rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)=\mathrm{3x}^{\mathrm{2}} \:+\mathrm{8x}\:>\mathrm{0}\:\mathrm{on}\left[\mathrm{1},\mathrm{2}\right]\:\Rightarrow\mathrm{f}\:\mathrm{is}\:\mathrm{increazing} \\ $$$$\mathrm{on}\:\left[\mathrm{1},\mathrm{2}\right]\:\mathrm{we}\:\mathrm{have}\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{5}−\mathrm{10}=−\mathrm{5}<\mathrm{0}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{2}\right)=\mathrm{8}+\mathrm{16}−\mathrm{10}=\mathrm{14}>\mathrm{0}\:\Rightarrow…
Question Number 133337 by mohammad17 last updated on 21/Feb/21 Commented by Dwaipayan Shikari last updated on 21/Feb/21 $${x}=\mathrm{3}\:{y}=\mathrm{1}\:{z}=\mathrm{2} \\ $$ Commented by mohammad17 last updated…
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Question Number 2258 by Filup last updated on 12/Nov/15 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sum}: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} {ix}^{{i}} ={x}−\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{4}} +… \\ $$ Commented by Filup last…
Question Number 2249 by Filup last updated on 11/Nov/15 $$\mathrm{With}\:\mathrm{linear}\:\mathrm{functions}\:{f}\left({x}\right)\:\mathrm{and}\:{g}\left({x}\right), \\ $$$$\mathrm{if}\:{f}\left({x}\right)\bot{g}\left({x}\right),\:\mathrm{then}: \\ $$$${m}_{{f}} {m}_{{g}} =−\mathrm{1}\:\:\:\:\mathrm{where}\:{m}_{{i}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{gradient} \\ $$$$\mathrm{of}\:\mathrm{function}\:{i}\left({x}\right). \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{that}\:\mathrm{therefore}\:\mathrm{mean}\:\mathrm{that},\:\mathrm{if}\:\mathrm{given} \\ $$$$\mathrm{function}\:\left(\mathrm{including}\:\mathrm{non}−\mathrm{linear}\right)\:{f}\left({x}\right),…
Question Number 2231 by Filup last updated on 10/Nov/15 $$\mathrm{For}\:{f}\left({x}\right)={x}! \\ $$$$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{defined}: \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:{f}'\left({x}\right) \\ $$$$\left(\mathrm{2}\right)\:\int{f}\left({x}\right){dx} \\ $$ Commented by Filup last updated…