Question Number 75929 by Rio Michael last updated on 21/Dec/19 $${Evaluate} \\ $$$$\underset{{x}\rightarrow−\infty} {\:\mathrm{lim}}\:\left[\sqrt{\mathrm{1}−{xe}^{{x}} }\:\right] \\ $$ Commented by kaivan.ahmadi last updated on 21/Dec/19 $${lim}_{{x}\rightarrow−\infty}…
Question Number 141463 by bramlexs22 last updated on 19/May/21 $$\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \left(\:\sqrt[{\mathrm{7}\:\:}]{\frac{{x}^{\mathrm{3}} +{x}}{{x}^{\mathrm{3}} +\mathrm{1}}}\:−\mathrm{cos}\:\frac{\mathrm{1}}{{x}}\right)? \\ $$ Commented by jcarlos last updated on 19/May/21 $$\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}}…
Question Number 10374 by ridwan balatif last updated on 06/Feb/17 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{\left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)\mathrm{sin}\left(\mathrm{3x}−\mathrm{3}\frac{\pi}{\mathrm{4}}\right)}{\mathrm{2}\left(\mathrm{1}−\mathrm{sin2x}\right)}=…? \\ $$ Answered by mrW1 last updated on 06/Feb/17 $${let}\:{u}={x}−\frac{\pi}{\mathrm{4}} \\ $$$${with}\:{x}\rightarrow\frac{\pi}{\mathrm{4}},\:{u}\rightarrow\mathrm{0} \\…
Question Number 75743 by Master last updated on 16/Dec/19 Commented by Master last updated on 16/Dec/19 $$\mathrm{work}\:\mathrm{without}\:\mathrm{lopart} \\ $$ Commented by $@ty@m123 last updated on…
Question Number 75694 by malwaan last updated on 15/Dec/19 $$\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}} \\…
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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}}}…