Question Number 66172 by mathmax by abdo last updated on 10/Aug/19 $$ \\ $$$${let}\:{A}_{{n}} =\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)\:\:\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:\frac{{ln}\left({A}_{{n}} \right)}{{n}} \\ $$ Commented by…
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…
Question Number 624 by 123456 last updated on 15/Feb/15 $$ \\ $$$${f}\left({x},{y}\right)=\sqrt{\mathrm{2}\left({x}+\sqrt{{x}^{\mathrm{2}} −{y}}\right)} \\ $$$${what}\:{is}\:{the}\:{domain}\:{of}\:{f}\left({x},{y}\right) \\ $$ Commented by prakash jain last updated on 12/Feb/15…
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 $$\left(\mathrm{1}\right)\:\mathrm{2f}\left(\mathrm{x}\right)−\mathrm{x}\:\mathrm{f}\left(\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}}\right)=\:\mathrm{3} \\ $$$$\:\mathrm{replacing}\:\mathrm{x}\:\mathrm{by}\:\frac{\mathrm{2x}+\mathrm{3}}{\mathrm{x}−\mathrm{2}} \\…
Question Number 66063 by mathmax by abdo last updated on 08/Aug/19 $${let}\:\:\:{x}^{\mathrm{2}} −{x}\:+{lnx}\:=\mathrm{0}\:\:\:\:\:{by}\:{using}\:{newton}\:{method}\:{find} \\ $$$${a}\:{approximate}\:{value}\:{of}\:{the}\:{roots}\:{of}\:{this}\:{equation}. \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
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 $${f}\left({x}+\frac{\mathrm{1}}{{x}}\right)={x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}}…
Question Number 66032 by mathmax by abdo last updated on 07/Aug/19 $${simplify}\:\:{w}_{{n}} =\left(\mathrm{1}+{in}\right)^{{n}} −\left(\mathrm{1}−{in}\right)^{{n}} \:{with}\:{n}\:{integr}\:{natural} \\ $$ Commented by mr W last updated on 08/Aug/19…
Question Number 66005 by mathmax by abdo last updated on 07/Aug/19 $${solve}\:\:\:{x}^{\mathrm{2}} {y}^{''} \:+{xy}^{'} −\mathrm{3}{y}\:=\mathrm{4}{e}^{−{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 431 by 123456 last updated on 25/Jan/15 $$\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}…