Question Number 143453 by yahy last updated on 14/Jun/21 Answered by Willson last updated on 14/Jun/21 $$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}^{\:\:\:\:\mathrm{n}} }\sqrt{\frac{\mathrm{n}^{\mathrm{n}} }{\mathrm{n}!}}\:=\:\frac{\mathrm{1}}{{e}} \\ $$ Commented by yahy…
Question Number 12382 by tawa last updated on 21/Apr/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{\mathrm{ln}\:\mathrm{cos}\left(\mathrm{3x}\right)}{\mathrm{ln}\:\mathrm{cos}\left(\mathrm{2x}\right)} \\ $$ Answered by ajfour last updated on 21/Apr/17 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{3}{x}\right)\right]}{\mathrm{ln}\:\left[\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right)\right]} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 143428 by mnjuly1970 last updated on 14/Jun/21 $$\:\:\:\:\: \\ $$$$…{Advanced}\:……{Mathematics}… \\ $$$$\:\:\:\:\:{Evaluate}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\::=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left(\pi{n}\right)}{{n}^{\mathrm{3}} }\:=? \\ $$ Answered by mindispower last…
Question Number 77856 by walidMTS last updated on 11/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {{l}im}\left(\frac{{e}^{{x}} −{x}−\mathrm{1}}{{x}}\right) \\ $$ Commented by mathmax by abdo last updated on 11/Jan/20 $${we}\:{have}\:{e}^{{x}} =\sum_{{n}=\mathrm{0}}…
Question Number 77852 by Math 1234 last updated on 11/Jan/20 $$\mathrm{5245} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 143339 by bramlexs22 last updated on 13/Jun/21 Commented by justtry last updated on 13/Jun/21 $${maybe}\:\mathrm{0} \\ $$ Answered by mathmax by abdo last…
Question Number 143252 by bramlexs22 last updated on 12/Jun/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}\:\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{5}} }\:=? \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$\frac{\mathrm{8}{x}−\mathrm{6}{x}\mathrm{sin}{x}+\mathrm{sin2}{x}}{{x}^{\mathrm{5}} }\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{x}}{{x}^{\mathrm{5}}…
Question Number 12094 by Joel576 last updated on 13/Apr/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{tan}\:\mathrm{5}{x}}{\mathrm{cos}\:\mathrm{2}{x}\:.\:\mathrm{cos}\:\mathrm{7}{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12062 by tawa last updated on 10/Apr/17 $$\underset{{x}\rightarrow\mathrm{y}} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{n}} \:−\:\mathrm{y}^{\mathrm{n}} }{\mathrm{x}\:−\:\mathrm{y}} \\ $$ Answered by ajfour last updated on 11/Apr/17 $$\boldsymbol{{x}}^{\boldsymbol{{n}}} −\boldsymbol{{y}}^{\boldsymbol{{n}}} =\left(\boldsymbol{{x}}−\boldsymbol{{y}}\right)\left(\boldsymbol{{x}}^{\boldsymbol{{n}}−\mathrm{1}}…
Question Number 77545 by aliesam last updated on 07/Jan/20 Terms of Service Privacy Policy Contact: info@tinkutara.com