Category: Limits

Question Number 80983 by jagoll last updated on 08/Feb/20 $$if\underset{x\to 0}{\lim }\frac{{ae}^x-b\sin x+{ce}^{-x}}{x\sin x}=2$$$$whatisa+b+c?$$ Commented by jagoll last updated on 09/Feb/20 $${i}\:{can}'{t}\:{solved}\:{this}\:{equation}.\:…

Question Number 146376 by iloveisrael last updated on 13/Jul/21 $$\underset{x\to 0}{\lim }\frac{1-\cos \mathrm{x}\cos 2\mathrm{x}\cos 3\mathrm{x}\dots \cos \mathrm{px}}{{\mathrm{x}}^2}=?$$ Answered by gsk2684 last updated on 13/Jul/21 $$\frac{0}{0}form,apply{L}^{\prime }Hopitalrule$$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}.\mathrm{cos}\:\mathrm{2}{x}…\mathrm{cos}\:{px}+\mathrm{cos}\:{x}.\left(\mathrm{2sin}\:\mathrm{2}{x}\right)\mathrm{cos}\:\mathrm{3}{x}…\mathrm{cos}\:{px}+..\:}{\mathrm{2}{x}}…

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}}…