Category: Limits

Question Number 28084 by tawa tawa last updated on 20/Jan/18 $$\underset{x\to \mathrm{\infty }}{\lim }(\mathrm{x}-{\log }_{\mathrm{e}}\mathrm{x})$$ Commented by çhëý böý last updated on 20/Jan/18 $$\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\:\left({x}−{lnx}\right)…

Question Number 159130 by metamorfose last updated on 13/Nov/21 $$f\in {\mathcal{C}}^0(\mathbb{R},\mathbb{R}),\frac{f\left(x\right)}{x}\underset{x\to +\mathrm{\infty }}{\to }0$$$$Does\underset{x\to +\mathrm{\infty }}{\lim }f(x+1)-f\left(x\right)exist?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 158894 by mathlove last updated on 10/Nov/21 Commented by cortano last updated on 10/Nov/21 $$\underset{x\to y}{\lim }\frac{{\left(\sqrt[3]{x}\right)}^2-{\left(\sqrt[3]{y}\right)}^2}{x-y}$$$$=\:\underset{{x}\rightarrow{y}} {\mathrm{lim}}\:\frac{\left(\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{y}}\right)\left(\sqrt[{\mathrm{3}}]{{x}}−\sqrt[{\mathrm{3}}]{{y}}\right)}{\left(\sqrt[{\mathrm{3}}]{{x}}−\sqrt[{\mathrm{3}}]{{y}}\right)\left(\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} }+\sqrt[{\mathrm{3}}]{{xy}}+\sqrt[{\mathrm{3}}]{{y}}\right)} \…

Question Number 27789 by abdo imad last updated on 14/Jan/18 $$find{lim}_{x->0}{(1+sinx)}^{\frac{1}{x}}.$$ Commented by abdo imad last updated on 15/Jan/18 $${we}\:{have}\:\left(\mathrm{1}+{sinx}\right)^{\frac{\mathrm{1}}{{x}}} \:=\:{e}^{\frac{\mathrm{1}}{{x}}{ln}\left(\mathrm{1}+{sinx}\right)}…

Question Number 27787 by abdo imad last updated on 14/Jan/18 $$find{lim}_{x->0}\frac{e^x-x-1}{x^2}.$$ Answered by prakash jain last updated on 14/Jan/18 $${e}^{{x}}…