Category: Limits

Question Number 174258 by blackmamba last updated on 28/Jul/22 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt{\sqrt{x^4-x^3}}-x=?$$ Answered by cortano1 last updated on 28/Jul/22 $$\:\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{4}} −{x}^{\mathrm{3}}…

Question Number 174152 by cortano1 last updated on 26/Jul/22 $$\underset{x\to 0}{\lim }\frac{1-\sin (\frac{\pi }{2}\cos x+2x)}{5x^2}=?$$ Answered by CElcedricjunior last updated on 26/Jul/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{sin}\left(\frac{\boldsymbol{\pi}}{\mathrm{2}}{cosx}+\mathrm{2}{x}\right)}{\mathrm{5}\boldsymbol{{x}}^{\mathrm{2}} }=\frac{\mathrm{0}}{\mathrm{0}}=\boldsymbol{{F}\mathrm{I}} \…

Question Number 174071 by alcohol last updated on 24/Jul/22 Answered by aleks041103 last updated on 24/Jul/22 $$.$$$$1.$$$${F}\left({x}\right)=\int_{\mathrm{0}} ^{\:{x}} \frac{{dt}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}=\int_{\mathrm{0}}…

Question Number 108469 by bemath last updated on 17/Aug/20 $$\frac{\subset \mathcal{B}e\mathcal{M}ath\supset }{\cap }$$$$\left(1\right)\underset{x\to 0}{\lim }\frac{1-\cos x\sqrt{\cos 2x}\sqrt{\cos 3x}\dots \sqrt{\cos nx}}{x^2}?$$$$\left(2\right)x^2{y}^{″}+{xy}^{\prime }-4y=0;y\left(1\right)=2and$$$$y^{\prime }\left(1\right)=0$$$$\left(3\right)findtheprobabilitythatapersonthrowingthree$$$$coinsatoncewillgetallthefaceor$$$${everything}\:{back}\:{for}\:{second}\:{time}\:{at}…

Question Number 42897 by Joel578 last updated on 04/Sep/18 Commented by Joel578 last updated on 04/Sep/18 $$\mathrm{For}\mathrm{question}\left(c\right),$$$$\underset{x\to 0}{\lim }G\left(x\right)=2\mathrm{or}\underset{x\to 0}{\lim }G\left(x\right)=0?$$ Answered by…