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Category: Relation and Functions

Question-175674

Question Number 175674 by infinityaction last updated on 05/Sep/22 Answered by mr W last updated on 05/Sep/22 $$−\frac{{b}}{\mathrm{2}{a}}=\mathrm{2}\:\Rightarrow{b}=−\mathrm{4}{a} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{4}{a}+\mathrm{2}{b}+{c}={c}−\mathrm{4}{a} \\ $$$${f}\left(\mathrm{1}\right)={a}+{b}+{c}={c}−\mathrm{3}{a}={f}\left(\mathrm{3}\right) \\ $$$${f}\left({f}\left(\mathrm{1}\right)\right)={f}\left({f}\left(\mathrm{2}\right)\right) \\…

If-is-an-even-function-defined-on-the-interval-5-5-then-a-value-of-x-satisfying-the-equation-f-x-f-x-1-x-2-is-a-1-5-2-b-3-5-2-c-1-5-2-d-3-5-2-

Question Number 44351 by Necxx last updated on 27/Sep/18 $${If}\:{is}\:{an}\:{even}\:{function}\:{defined}\:{on} \\ $$$${the}\:{interval}\:\left(−\mathrm{5},\mathrm{5}\right)\:{then}\:{a}\:{value} \\ $$$${of}\:{x}\:{satisfying}\:{the}\:{equation} \\ $$$${f}\left({x}\right)={f}\left(\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\right)\:{is} \\ $$$$\left.{a}\left.\right)\left.\frac{−\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\:{b}\right)\frac{−\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}}\:{c}\right)\frac{−\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}\: \\ $$$$\left.{d}\right)\frac{−\mathrm{3}−\sqrt{\mathrm{5}}}{\mathrm{2}_{} } \\ $$ Commented by…

let-u-n-0-1-x-n-artan-nx-dx-1-lim-u-n-2-nature-of-u-n-3-calculate-u-n-4-equivalent-of-u-n-

Question Number 174938 by Mathspace last updated on 14/Aug/22 $${let}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} {artan}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right){lim}\:{u}_{{n}} ? \\ $$$$\left.\mathrm{2}\right){nature}\:{of}\:\Sigma\:{u}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{u}_{{n}} \\ $$$$\left.\mathrm{4}\right){equivalent}\:{of}\:{u}_{{n}} ? \\…