Category: Limits

Question Number 183936 by universe last updated on 31/Dec/22 Answered by Ar Brandon last updated on 31/Dec/22 $$\mathscr{L}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\overset{{n}} {\:}{C}_{{k}} }\right)^{{n}} =\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{k}=\mathrm{1}}…

Question Number 118327 by bramlexs22 last updated on 17/Oct/20 $$\underset{x\to 1}{\lim }\frac{x-\sqrt{2-x^2}}{2x-\sqrt{2+2x^2}}?$$ Answered by TANMAY PANACEA last updated on 17/Oct/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}}…

Question Number 118247 by bemath last updated on 16/Oct/20 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt[4]{1+x^4}-\sqrt[5]{1+x^5}=?$$ Answered by bobhans last updated on 16/Oct/20 $${solve}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{4}}]{\mathrm{1}+{x}^{\mathrm{4}} }\:−\:\sqrt[{\mathrm{5}\:}]{\mathrm{1}+{x}^{\mathrm{5}}…

Question Number 118140 by bemath last updated on 15/Oct/20 $$\underset{x\to 0}{\lim }\frac{\left[x^2\right]}{2x}=?$$ Answered by TANMAY PANACEA last updated on 15/Oct/20 $${let}\:{x}=\mathrm{0}.\mathrm{9}\:\:{x}^{\mathrm{2}} =\mathrm{0}.\mathrm{81}\:\:\left[\mathrm{0}.\mathrm{81}\right]=\mathrm{0} \…

Question Number 118088 by bobhans last updated on 15/Oct/20 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{\mathrm{x}.\sqrt{{\mathrm{x}}^2+1}.\sqrt[3]{{\mathrm{x}}^3+1}}{{(2\mathrm{x}+1)}^3}=?$$ Answered by bemath last updated on 15/Oct/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}.\sqrt{\mathrm{x}^{\mathrm{2}}…