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Category: Relation and Functions

find-lim-n-1-n-2-sin-1-n-2-2sin-4-n-2-n-1-sin-n-1-2-n-2-

Question Number 66171 by mathmax by abdo last updated on 10/Aug/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left\{{sin}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)+\mathrm{2}{sin}\left(\frac{\mathrm{4}}{{n}^{\mathrm{2}} }\right)+….\left({n}−\mathrm{1}\right){sin}\left(\frac{\left({n}−\mathrm{1}\right)^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)\right\} \\ $$ Commented by mathmax by abdo…

What-is-f-x-if-2f-x-x-f-2x-3-x-2-3-when-x-2-

Question Number 131641 by liberty last updated on 07/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{if}\::\:\mathrm{2f}\left(\mathrm{x}\right)−\mathrm{x}\:\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}}\right)=\mathrm{3} \\ $$$$\mathrm{when}\:\mathrm{x}\neq\:\mathrm{2}\:?\: \\ $$ Answered by EDWIN88 last updated on 07/Feb/21 $$\left(\mathrm{1}\right)\:\mathrm{2f}\left(\mathrm{x}\right)−\mathrm{x}\:\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}}\right)=\:\mathrm{3} \\ $$$$\:\mathrm{replacing}\:\mathrm{x}\:\mathrm{by}\:\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}} \\…

if-f-x-1-x-x-3-1-x-3-then-faind-f-1-x-

Question Number 131573 by mathlove last updated on 06/Feb/21 $$\:{if}\:\:\:\:{f}\left({x}+\frac{\mathrm{1}}{{x}}\right)={x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:\:\:\:\:{then}\:\:{faind}\:\: \\ $$$${f}\left(\frac{\mathrm{1}}{{x}}\right)=? \\ $$ Answered by rs4089 last updated on 06/Feb/21 $${f}\left({x}+\frac{\mathrm{1}}{{x}}\right)={x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}}…

given-x-n-1-1-3-x-n-x-0-2-proof-that-a-0-lt-x-n-2-n-N-b-x-n-is-decreasing-c-lim-n-x-n-

Question Number 431 by 123456 last updated on 25/Jan/15 $$\mathrm{given} \\ $$$${x}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{3}−{x}_{{n}} } \\ $$$${x}_{\mathrm{0}} =\mathrm{2} \\ $$$$\mathrm{proof}\:\mathrm{that} \\ $$$$\mathrm{a}.\mathrm{0}<{x}_{{n}} \leqslant\mathrm{2},{n}\in\mathbb{N} \\ $$$$\mathrm{b}.{x}_{{n}} \:\mathrm{is}\:\mathrm{decreasing}…