Category: Limits

Question Number 80792 by john santu last updated on 06/Feb/20 $$\underset{n=1}{\prod ^{\mathrm{\infty }}}[\frac{2n}{2n-1}.\frac{2n}{2n+1}]=?$$ Answered by mind is power last updated on 06/Feb/20 $${ln}\left(\underset{{n}\geqslant\mathrm{1}}…

Question Number 80748 by jagoll last updated on 06/Feb/20 $$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{x!}{x^x}\right)}^{\frac{1}{x}}=?$$ Commented by john santu last updated on 06/Feb/20 $${let}\:{y}\:=\:\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\left(\frac{{x}!}{{x}^{{x}}…

Question Number 146263 by bemath last updated on 12/Jul/21 $$\underset{x\to -\mathrm{\infty }}{\lim }(-2x+1-\sqrt{4x^2-5x+8})=?$$ Answered by gsk2684 last updated on 12/Jul/21 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\left(−\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} −\left(\mathrm{4}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{8}\right)}{−\mathrm{2}{x}+\mathrm{1}+\sqrt{\mathrm{4}{x}^{\mathrm{2}}…

Question Number 80718 by TawaTawa last updated on 05/Feb/20 $$\mathrm{Evaluate}:\underset{x\to 0}{\lim }\frac{\mathrm{x}}{\mid \mathrm{x}\mid }$$ Commented by mind is power last updated on 05/Feb/20 $$\mid x\mid =\{\begin{array}{l}x,x>0\\ -x,x<0\end{array}$$$$\Rightarrow\underset{{x}\rightarrow\mathrm{0}^{+}…

Question Number 80690 by ahmadshahhimat775@gmail.com last updated on 05/Feb/20 Commented by jagoll last updated on 05/Feb/20 $$\underset{x\to e}{\lim }\frac{xlnx-x}{2-2lnx}=\underset{x\to e}{\lim }\frac{x(lnx-1)}{-2(lnx-1)}=$$$$-\frac{e}{2}$$ Commented by…