Category: Limits

Question Number 131825 by liberty last updated on 09/Feb/21 $$\underset{\mathrm{n}=1}{\sum ^{\mathrm{\infty }}}\frac{2\mathrm{n}-1}{2^{\mathrm{n}}}?$$ Answered by mr W last updated on 09/Feb/21 $${method}\:\mathrm{1} \…

Question Number 131769 by liberty last updated on 08/Feb/21 $$\underset{x\to \pi /2}{\lim }\frac{2^{-\cos \mathrm{x}}-1}{\mathrm{x}(\mathrm{x}-\frac{\pi }{2})}=?$$ Answered by bemath last updated on 08/Feb/21 $$\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{x}}\:.\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{2}^{\mathrm{sin}\:\left(\mathrm{x}−\frac{\pi}{\mathrm{2}}\right)} −\mathrm{1}}{\mathrm{x}−\frac{\pi}{\mathrm{2}}}\:=…

Question Number 585 by 123456 last updated on 02/Feb/15 $$f_n\left(x\right)={(1+\frac{x}{n})}^{nx},n\in {\mathbb{N}}^{\ast },x\in \mathbb{R},x⩾0$$$$\underset{n\to +\mathrm{\infty }}{\lim }{f}_n\left(x\right)=$$ Answered by prakash jain last updated…

Question Number 66084 by F_Nongue last updated on 09/Aug/19 $$Howtosolvethislimit?$$$$\underset{x\to \mathrm{\infty }}{lim}{(7x+\frac{2}{x})}^x$$ Commented by mathmax by abdo last updated on 09/Aug/19 $${let}\:{A}\left({x}\right)\:=\left(\mathrm{7}{x}+\frac{\mathrm{2}}{{x}}\right)^{{x}}…

Question Number 131548 by liberty last updated on 06/Feb/21 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\sqrt{\mathrm{n}}\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\cos {}^{2\mathrm{n}+1}\left(\theta \right)\mathrm{d}\theta =?$$ Answered by rs4089 last updated on 06/Feb/21 $$\frac{\pi\sqrt{\pi}}{\mathrm{2}} \…