Category: Limits

Question Number 129385 by Adel last updated on 15/Jan/21 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{1}{\sqrt{\mathrm{n}}}\frac{}{\sqrt{\mathrm{n}+1}}+\frac{}{\sqrt{\mathrm{n}}}\frac{1}{\sqrt{\mathrm{n}+2}}\frac{}{}+\frac{}{\sqrt{\mathbf{n}}}\frac{}{\sqrt{\mathbf{n}+3}}\frac{1}{}\frac{}{}+\dots \dots \dots \dots ..+\frac{}{\sqrt{\mathrm{n}}}\frac{1}{\sqrt{\mathrm{n}+\mathrm{n}}}\frac{}{}=?$$$$whatanswer$$ Answered by Dwaipayan Shikari last updated on 15/Jan/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}}…

Question Number 129211 by bramlexs22 last updated on 13/Jan/21 $$\underset{x\to 0}{\lim }\frac{1}{\cos {\left(\sqrt{\mathrm{x}}\right)}^{\frac{1}{\mathrm{x}}}}=?$$ Answered by liberty last updated on 13/Jan/21 $$\:\mathcal{L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{cos}\:\left(\sqrt{\mathrm{x}}\:\right)^{\frac{\mathrm{1}}{\mathrm{x}}} } \…

Question Number 63579 by Tawa1 last updated on 05/Jul/19 $$\underset{x\to 0}{\lim }\frac{2^{\sec \left(\mathrm{x}\right)}-2^{\cos \left(\mathrm{x}\right)}}{{\mathrm{x}}^2}$$ Commented by Prithwish sen last updated on 05/Jul/19 $$\because\:\mathrm{form}\:\frac{\mathrm{0}}{\mathrm{0}\:}\:\mathrm{applying}\:\mathrm{L}'\mathrm{Hopital}…

Question Number 129086 by Ar Brandon last updated on 12/Jan/21 $$\underset{\mathrm{x}\to 0}{\lim }\frac{1}{\mathrm{x}}\ln \left(\frac{{\mathrm{e}}^{\mathrm{x}}-1}{\mathrm{x}}\right)$$ Answered by Dwaipayan Shikari last updated on 12/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{log}\left(\frac{{e}^{{x}}…

Question Number 128908 by bramlexs22 last updated on 11/Jan/21 $$\underset{x\to \mathrm{\infty }}{\lim }(\mathrm{x}\sqrt{{\mathrm{x}}^2+4}-\sqrt{{\mathrm{x}}^4+16})=?$$ Answered by Dwaipayan Shikari last updated on 11/Jan/21 $$\left({x}^{\mathrm{2}} \sqrt{\mathrm{1}+\frac{\mathrm{4}}{{x}^{\mathrm{2}}…