Category: Limits

Question Number 117147 by bemath last updated on 10/Oct/20 $$\underset{x\to 0}{\lim }{\left(\frac{\cosh \left(2\mathrm{x}\right)}{\cosh \left(\mathrm{x}\right)}\right)}^{\frac{1}{{\mathrm{x}}^2}}=?$$ Answered by Olaf last updated on 10/Oct/20 $$\mathrm{cosh}{u}\:\underset{\mathrm{0}} {\sim}\:\mathrm{1}+\frac{{u}^{\mathrm{2}} }{\mathrm{2}}…

Question Number 182649 by amin96 last updated on 12/Dec/22 $$\mathit{f}(\mathit{x};\mathit{y})=\frac{{\mathit{x}}^2+{\mathit{y}}^2}{{\mathit{x}}^2+{\mathit{y}}^4}$$$$\underset{x\to \mathrm{\infty }}{\lim }\left(\underset{y\to 0}{\lim }\mathit{f}(\mathit{x};\mathit{y})\right)=?$$$$\underset{\mathit{y}\to \mathrm{\infty }}{\lim }\left(\underset{x\to \mathrm{\infty }}{\lim }\mathit{f}(\mathit{x};\mathit{y})\right)=?$$ Answered…

Question Number 182629 by universe last updated on 12/Dec/22 $$\underset{\mathbf{n}=2}{\prod ^{\mathrm{\infty }}}\mathbf{e}{(1-\frac{1}{{\mathbf{n}}^2})}^{{\mathbf{n}}^2}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 117052 by bemath last updated on 09/Oct/20 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt{4\mathrm{x}+\sqrt{4\mathrm{x}+\sqrt{4\mathrm{x}+\sqrt{4\mathrm{x}}}}}-\sqrt{4\mathrm{x}}=?$$ Answered by bobhans last updated on 09/Oct/20 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt{4\mathrm{x}(1+\frac{\sqrt{4\mathrm{x}+\sqrt{4\mathrm{x}+\sqrt{4\mathrm{x}}}}}{4\mathrm{x}})}-\sqrt{4\mathrm{x}}$$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{4x}}\:\left[\:\sqrt{\mathrm{1}+\sqrt{\frac{\mathrm{1}}{\mathrm{4x}}+\sqrt{\frac{\mathrm{1}}{\left(\mathrm{4x}\right)^{\mathrm{3}}…

Question Number 182560 by universe last updated on 11/Dec/22 $$\underset{x\to 0}{\lim }\frac{1}{x^2}-{\cot }^{2}x=?$$ Answered by cortano1 last updated on 11/Dec/22 $$\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{x}−\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:.\:\underset{{x}\rightarrow\mathrm{0}}…