Question Number 75597 by aliesam last updated on 13/Dec/19 Commented by mathmax by abdo last updated on 13/Dec/19 $${let}\:{f}\left({x}\right)=\frac{\left({cosx}\right)^{\frac{\mathrm{1}}{{m}}} −\left({cosx}\right)^{\frac{\mathrm{1}}{{n}}} }{{x}^{\mathrm{2}} }\:\:{we}\:{have} \\ $$$${cosx}\:\sim\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:\Rightarrow\left({cosx}\right)^{\frac{\mathrm{1}}{{m}}}…
Question Number 141127 by bobhans last updated on 16/May/21 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{i}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{{n}}{\left({n}+{i}\right)^{\mathrm{2}} }\:=?\: \\ $$ Answered by Ar Brandon last updated on 16/May/21 $$\mathscr{L}=\underset{\mathrm{n}\rightarrow\infty}…
Question Number 141124 by iloveisrael last updated on 16/May/21 Answered by bobhans last updated on 16/May/21 Answered by EDWIN88 last updated on 16/May/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{sin}\:\mathrm{x}\right)+\sqrt{\mathrm{x}^{\mathrm{4}}…
Question Number 10035 by Sri rama jeyam last updated on 21/Jan/17 $$\mathrm{is}\:\mathrm{cos}\left(\mathrm{7x}+\mathrm{i5y}\right)\:\mathrm{analytic}\:\mathrm{function}\:\mathrm{or}\:\mathrm{not} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75553 by aliesam last updated on 12/Dec/19 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{\mathrm{1}}{{x}}\left(\frac{\mathrm{1}}{{sin}\left({x}\right)}−\frac{\mathrm{3}}{{sin}\left(\mathrm{3}{x}\right)}\right) \\ $$ Commented by mathmax by abdo last updated on 12/Dec/19 $${f}\left({x}\right)=\frac{{sin}\left(\mathrm{3}{x}\right)−\mathrm{3}{sinx}}{{x}\:{sin}\left({x}\right){sin}\left(\mathrm{3}{x}\right)}\:\:{we}\:{have}\:{sinx}=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}}…
Question Number 75547 by TawaTawa last updated on 12/Dec/19 $$\:\:\:\:\:\:\mathrm{Evaluate}:\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{5n}\:+\:\mathrm{1}}\right) \\ $$ Commented by mind is power last updated on 13/Dec/19 $$\mathrm{mor}\:\mathrm{generaly} \\…
Question Number 141077 by Opredador last updated on 15/May/21 $$\:{Calculate}\:\:{the}\:\:\underset{{x}\rightarrow\mathrm{1}} {{lim}}\left(\frac{\sqrt{{x}^{{x}} }\:−\:\sqrt{{x}}}{{x}^{{x}} \:−\:{x}}\right). \\ $$ Answered by EDWIN88 last updated on 15/May/21 $$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}^{\mathrm{x}} }−\sqrt{\mathrm{x}}}{\mathrm{x}^{\mathrm{x}}…
Question Number 75468 by aliesam last updated on 11/Dec/19 $$\underset{{n}\rightarrow\infty} {{lim}}\sqrt{\frac{\mathrm{2}{n}^{\mathrm{2}} −\mathrm{5}{n}+\mathrm{3}}{{n}^{\mathrm{5}} +\mathrm{1}}} \\ $$ Commented by MJS last updated on 11/Dec/19 $${P}_{{n}} \left({x}\right)={c}_{{n}} {x}^{{n}}…
Question Number 9929 by ridwan balatif last updated on 16/Jan/17 Answered by mrW1 last updated on 18/Jan/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{4}{x}\centerdot\mathrm{tan}^{\mathrm{2}} \:\mathrm{3}{x}+\mathrm{6}{x}^{\mathrm{2}} }{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{sin}\:\mathrm{3}{x}\centerdot\mathrm{cos}\:\mathrm{2}{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4}\left(\frac{\mathrm{sin}\:\mathrm{4}{x}}{\mathrm{4}{x}}\right)\mathrm{tan}^{\mathrm{2}}…
Question Number 75469 by aliesam last updated on 11/Dec/19 $$\underset{{n}\rightarrow\infty} {{lim}}\left(\:\sqrt{{n}+\mathrm{1}}−\sqrt{{n}}\:\right) \\ $$ Commented by MJS last updated on 11/Dec/19 $$\mathrm{0} \\ $$$$\mathrm{because}\:{n}+\mathrm{1}\sim{n}\:\mathrm{for}\:\mathrm{large}\:{n} \\ $$…