Category: Limits

Question Number 82425 by zainal tanjung last updated on 21/Feb/20 $$\mathrm{Lim}{\left(\frac{1}{\mathrm{ex}}\right)}^{6\mathrm{x}}=\dots ..$$$$\mathrm{x}\to 0$$ Commented by abdomathmax last updated on 21/Feb/20 $${let}\:{f}\left({x}\right)=\left(\frac{\mathrm{1}}{{ex}}\right)^{\mathrm{6}{x}} \:\Rightarrow{f}\left({x}\right)={e}^{−\mathrm{6}{xln}\left({ex}\right)}…

Question Number 147738 by liberty last updated on 23/Jul/21 $$\underset{x\to 0}{\lim }\frac{\arctan x-\arcsin x}{\sin {}^{3}x}=?$$ Answered by gsk2684 last updated on 23/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}^{−\mathrm{1}} {x}−\mathrm{sin}^{−\mathrm{1}} {x}}{\mathrm{sin}\:^{\mathrm{3}}…

Question Number 82160 by M±th+et£s last updated on 18/Feb/20 $$provethat$$$$\underset{x\to \mathrm{\infty }}{lim}{n}^2\sqrt{(1-cos\left(\frac{1}{n}\right)\sqrt{(1-cos\frac{1}{n})\sqrt{(1-cos\frac{1}{n})\dots }}}=\frac{1}{2}$$ Answered by MJS last updated on 18/Feb/20 $${w}=\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\frac{\mathrm{1}}{{n}}\right)\sqrt{…}}} \…

Question Number 147459 by liberty last updated on 21/Jul/21 $$\underset{x\to 0}{\lim }\frac{\sqrt{1+x^2}\sqrt[3]{8+x^3}-2}{x^2}=?$$ Answered by mathmax by abdo last updated on 21/Jul/21…

Question Number 81853 by jagoll last updated on 16/Feb/20 $$\underset{x\to \mathrm{\infty }}{\lim }\left\{n\underset{0}{\stackrel{1}{\int }}\frac{x^n}{x^3+1}dx\right\}=?$$ Commented by john santu last updated on 16/Feb/20…