Question Number 66317 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{ln}\left({cosx}\right)}{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)} \\ $$ Commented by kaivan.ahmadi last updated on 12/Aug/19 $$\equiv{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left({cosx}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\overset{{hop}}…
Question Number 66304 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{ln}\left({x}+\mathrm{1}+{sin}\left(\pi{x}\right)\right)}{{xsin}\left(\mathrm{2}{x}\right)} \\ $$ Answered by kaivan.ahmadi last updated on 12/Aug/19 $$\equiv{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left({x}+\mathrm{1}+\pi{x}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\:\overset{{hop}}…
Question Number 680 by 123456 last updated on 23/Feb/15 $${find}\:{all}\:{f}:\mathbb{N}\rightarrow\mathbb{N}\:{such}\:{that} \\ $$$${f}\left[{n}+{f}\left({n}\right)\right]=\mathrm{2}{f}\left({n}\right) \\ $$ Answered by prakash jain last updated on 23/Feb/15 $${f}\left({n}\right)={kn}\:+{k}_{\mathrm{1}} \\ $$$${f}\left({n}+{kn}+{k}_{\mathrm{1}}…
Question Number 677 by prakash jain last updated on 22/Feb/15 $$\mathrm{Find}\:\mathrm{all}\:{f}:\:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}^{\mathrm{2}} +{yf}\left({x}\right)\right)={xf}\left({x}+{y}\right) \\ $$ Commented by 123456 last updated on 22/Feb/15 $${suposing}\:{f}\left({x}\right)={ax}+{b} \\…
Question Number 655 by 123456 last updated on 19/Feb/15 $${f}\left({z}\right)=\frac{\mathrm{1}−\frac{\mathrm{1}−{z}^{\mathrm{2}} }{\mathrm{2}+{z}^{\mathrm{2}} }}{\mathrm{2}+\frac{\mathrm{1}−{z}^{\mathrm{2}} }{\mathrm{2}+{z}^{\mathrm{2}} }} \\ $$$$\frac{{f}\left(\mathrm{0}\right)+{f}\left(\mathrm{1}\right)}{\mathrm{2}}−{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=? \\ $$ Answered by prakash jain last updated on…
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:…