Category: Limits

Question Number 94730 by i jagooll last updated on 20/May/20 Answered by john santu last updated on 20/May/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\mathrm{e}^{\mathrm{ln}\left(\mathrm{x}\right)^{\mathrm{sin}\:\mathrm{x}} } =\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{e}^{\mathrm{sin}\:\mathrm{x}.\:\mathrm{ln}\left(\mathrm{x}\right)} \…

Question Number 94723 by john santu last updated on 20/May/20 $$\underset{x\to 0}{\lim }\frac{\underset{0}{\stackrel{x^2}{\int }}\sqrt{4+t^3}dt}{x^2}?$$ Answered by i jagooll last updated…

Question Number 160244 by cortano last updated on 26/Nov/21 $$L\underset{x\to 0}{im}\left(\frac{{\tan }^{-1}\left(x\right)-\tan \left(x\right)}{{\sin }^{-1}\left(x\right)-\sin \left(x\right)}\right)=?$$ Answered by FongXD last updated on 26/Nov/21 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}−\mathrm{tanx}}{\mathrm{x}^{\mathrm{3}}…

Question Number 29158 by abdo imad last updated on 04/Feb/18 $$find{lim}_{x\to 1}\frac{\sqrt{3+\sqrt{2x-1}}-2}{\sqrt{2+\sqrt{3x+1}}-\sqrt{x+3}}.$$ Commented by abdo imad last updated on 09/Feb/18 $$inthiscaseitsbettertousehospitaltheoremletput$$$${u}\left({x}\right)=\sqrt{\mathrm{3}+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\:−\mathrm{2}\:{and}\:{v}\left({x}\right)=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}{x}+\mathrm{1}}}\:\:−\sqrt{{x}+\mathrm{3}}…

Question Number 160218 by qaz last updated on 26/Nov/21 $$\underset{\mathrm{x}\to +\mathrm{\infty }}{\lim }\frac{{\int }_0^{\mathrm{x}}{\left(\arctan \mathrm{t}\right)}^2\mathrm{dt}}{\sqrt{1+{\mathrm{x}}^2}}=?$$ Answered by mathmax by abdo last updated on…