Question Number 239 by 123456 last updated on 25/Jan/15 $$\mathrm{find}\:\mathrm{f}\left(\mathrm{10}\right)\:\mathrm{given} \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\mathrm{f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)+\mathrm{f}\left(\mathrm{x}−\mathrm{2}\right),\mathrm{x}>\mathrm{1},\mathrm{x}\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{2}\right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\mathrm{f}\left(\mathrm{x}−\mathrm{2}\right),\mathrm{x}>\mathrm{1},\mathrm{x}\equiv\mathrm{1}\left(\mathrm{mod}\:\mathrm{2}\right) \\ $$ Answered by prakash jain last…
Question Number 131295 by EDWIN88 last updated on 03/Feb/21 $${Find}\:{domain}\:{of}\:{function}\: \\ $$$${f}\left({x}\right)=\:\sqrt{\frac{\mathrm{cos}\:{x}−\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{6}+\mathrm{35}{x}−\mathrm{6}{x}^{\mathrm{2}} }}\: \\ $$ Answered by liberty last updated on 03/Feb/21 $$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\frac{\mathrm{cos}\:\mathrm{x}−\mathrm{1}/\mathrm{2}}{\mathrm{6}+\mathrm{35x}−\mathrm{6x}^{\mathrm{2}} }}\: \\…
Question Number 131285 by EDWIN88 last updated on 03/Feb/21 $${How}\:{many}\:{curves}\:{with}\:{equation} \\ $$$${Ax}^{\mathrm{2}} −\left(\frac{{B}}{\mathrm{2}}{y}\right)^{\mathrm{2}} =\:\mathrm{0}\:{with}\:{A}\:{and}\:{B}\:{two} \\ $$$${different}\:{numbers}\:{are}\:{selected}\: \\ $$$${from}\:{the}\:{set}\:\left\{\:−\mathrm{3},−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{3}\:\right\}\:? \\ $$$$\left({a}\right)\:\mathrm{8}\:\:\:\:\:\:\left({b}\right)\mathrm{10}\:\:\:\:\:\left({c}\right)\mathrm{12} \\ $$$$\left({d}\right)\:\mathrm{22}\:\:\:\left({e}\right)\:\mathrm{20} \\ $$ Answered…
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Question Number 65674 by mathmax by abdo last updated on 01/Aug/19 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\frac{{n}}{\left({n}+\mathrm{1}\right)^{\mathrm{2}} \left({n}−\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 65677 by mathmax by abdo last updated on 01/Aug/19 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{\:\sqrt{{k}^{\mathrm{2}} +{k}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\left({S}_{{n}} \right)\:{is}\:{convergent}. \\ $$ Terms…
Question Number 65673 by mathmax by abdo last updated on 01/Aug/19 $${find}\:\sum_{{n}=\mathrm{2}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last…
Question Number 65664 by mathmax by abdo last updated on 01/Aug/19 $${solve}\:\frac{\sqrt{\mathrm{1}−{x}}−\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\:\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{2}{x}+\mathrm{1}}}\:=\frac{{x}+\mathrm{1}}{\mathrm{3}} \\ $$ Answered by MJS last updated on 01/Aug/19 $$\frac{\sqrt{\mathrm{1}−{x}}−\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\:\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{2}{x}+\mathrm{1}}}=\frac{\left(\sqrt{\mathrm{1}−{x}}−\sqrt{\mathrm{2}{x}+\mathrm{1}}\right)^{\mathrm{2}} }{\left(\sqrt{\mathrm{1}−{x}}+\sqrt{\mathrm{2}{x}+\mathrm{1}}\right)\left(\sqrt{\mathrm{1}−{x}}−\sqrt{\mathrm{2}{x}+\mathrm{1}}\right)}= \\ $$$$=\frac{{x}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{1}−{x}}\sqrt{\mathrm{2}{x}+\mathrm{1}}}{−\mathrm{3}{x}}=−\frac{{x}+\mathrm{2}}{\mathrm{3}{x}}+\frac{\mathrm{2}\sqrt{\mathrm{1}−{x}}\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{3}{x}}…
Question Number 144001 by mnjuly1970 last updated on 20/Jun/21 Answered by Dwaipayan Shikari last updated on 20/Jun/21 $$\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{\frac{\mathrm{1}}{\mathrm{1}}} \left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \left(\mathrm{1}+\frac{\mathrm{3}}{{n}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} …={y} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}}…
Question Number 143987 by liberty last updated on 20/Jun/21 $${If}\:{f}\left({x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{6}\right)+{f}\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}\right)=\mathrm{2}{x} \\ $$$$\forall{x}\in{R}\:{th}\mathrm{e}{n}\:{f}\left(−\mathrm{3}\right)+{f}\left(\mathrm{9}\right)−\mathrm{5}{f}\left(\mathrm{1}\right)=? \\ $$ Answered by mitica last updated on 20/Jun/21 $${x}=\mathrm{1}\Rightarrow{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{1}\right)=\mathrm{2}\Rightarrow{f}\left(\mathrm{1}\right)=\mathrm{1} \\…