Question Number 75694 by malwaan last updated on 15/Dec/19 $$\boldsymbol{{prove}}\:\boldsymbol{{that}}\: \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\infty} {\boldsymbol{{lim}}}\:\boldsymbol{{x}}^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} \:=\mathrm{1} \\ $$ Answered by vishalbhardwaj last updated on 15/Dec/19 $$\left({as}\:{x}\rightarrow\infty\:\mathrm{then}\:\frac{\mathrm{1}}{{x}}\:\rightarrow\:\mathrm{0}\right) \\…
Question Number 10137 by malwaan last updated on 26/Jan/17 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\:\frac{{sin}\:{x}^{{m}} }{{sin}^{{n}} \:{x}}\:\:{n};{m}\:\in\mathbb{Z} \\ $$ Answered by mrW1 last updated on 26/Jan/17 $$\underset{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 10094 by Tawakalitu ayo mi last updated on 23/Jan/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\:\:\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\:\mathrm{f}_{\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{L}_{\mathrm{1}} \:\:\mathrm{and}\:\: \\ $$$$\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\:\:\mathrm{f}_{\mathrm{2}} \left(\mathrm{x}\right)\:=\:\mathrm{L}_{\mathrm{2}} \:\mathrm{then}\:\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\left[\mathrm{f}_{\mathrm{1}} \left(\mathrm{x}\right)+\mathrm{f}_{\mathrm{2}} \left(\mathrm{x}\right)\right]\:=\:\mathrm{L}_{\mathrm{1}} +\mathrm{L}_{\mathrm{2}} \\…
Question Number 141149 by Dan last updated on 16/May/21 $${lim}_{{x}\rightarrow\infty} \underset{{i}=\mathrm{0}} {\overset{{x}−\mathrm{1}} {\sum}}\frac{{x}}{\left({x}+{i}\right)} \\ $$ Answered by mr W last updated on 16/May/21 $$\frac{{x}}{{x}+{x}}<\frac{{x}}{{x}+{i}}<\frac{{x}}{{x}} \\…
Question Number 141148 by Dan last updated on 16/May/21 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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}}…