Category: Limits

Question Number 82950 by jagoll last updated on 26/Feb/20 $$$$$$\underset{x\to 0}{\lim }\frac{\sqrt[3]{1+\tan \mathrm{x}}-\sqrt[3]{1+\sin \mathrm{x}}}{{\mathrm{x}}^3}=$$ Commented by mathmax by abdo last updated on 26/Feb/20…

Question Number 148439 by liberty last updated on 28/Jul/21 $$\underset{x\to 2}{\lim }\frac{\sqrt{\mathrm{x}+2}\sqrt[3]{\mathrm{x}+6}-{\mathrm{x}}^2}{\mathrm{x}-2}=?$$ Answered by dumitrel last updated on 28/Jul/21 $$\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{\sqrt{{x}+\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{{x}+\mathrm{6}}−\mathrm{2}\right)}{{x}−\mathrm{2}}+\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{\mathrm{2}\left(\sqrt{{x}+\mathrm{2}}−\mathrm{2}\right)}{{x}−\mathrm{2}}−\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{{x}^{\mathrm{2}}…

Question Number 82815 by M±th+et£s last updated on 24/Feb/20 $$\underset{x\to 0^{+}}{lim}\frac{1}{{(1+\frac{1}{x})}^{\frac{1}{ln\left(x\right)}}}=?$$ Commented by mathmax by abdo last updated on 24/Feb/20 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{−\frac{\mathrm{1}}{{lnx}}}…

Question Number 148328 by liberty last updated on 27/Jul/21 $$\underset{x\to 0}{\lim }\frac{\sin 2\mathrm{x}+2\sin {}^2\mathrm{x}-2\sin \mathrm{x}}{\cos \mathrm{x}-\cos {}^2\mathrm{x}}=?$$ Answered by EDWIN88 last updated on 27/Jul/21 Answered by mathmax…

Question Number 82761 by TANMAY PANACEA last updated on 24/Feb/20 $$\underset{x\to 0}{\lim }\frac{{\left(cosx\right)}^{\frac{1}{m}}-{\left(cosx\right)}^{\frac{1}{n}}}{x^2}\left[wheremandninteger\right]$$ Commented by mr W last updated on 24/Feb/20…