Category: Limits

Question Number 87168 by mathocean1 last updated on 03/Apr/20 $$Calculatetheselimits:$$$$Pleasesirsdetail$$ Commented by john santu last updated on 03/Apr/20 $$\mathrm{a})\mathrm{change}\mathrm{x}\Rightarrow -\mathrm{t}$$$$\underset{\mathrm{t}\rightarrow\infty}…

Question Number 87105 by Chi Mes Try last updated on 02/Apr/20 Commented by mathmax by abdo last updated on 03/Apr/20 $$letf\left(x\right)=\frac{x}{x-1}-\frac{1}{lnx}\Rightarrow f\left(x\right)=\frac{xln\left(x\right)-x+1}{(x-1)ln\left(x\right)}wedothechangement$$$$x-1=t\Rightarrow f\left(x\right)=\frac{(t+1)ln(1+t)+1-(t+1)}{tln(1+t)}=g\left(t\right)$$$$=\frac{\left({t}+\mathrm{1}\right){ln}\left(\mathrm{1}+{t}\right)−{t}}{{tln}\left(\mathrm{1}+{t}\right)}\:\:\left({x}\rightarrow\mathrm{1}\:\Rightarrow{t}\rightarrow\mathrm{0}\right)\:{so}…

Question Number 87061 by john santu last updated on 02/Apr/20 $$\underset{x\to 0}{\lim }\frac{\cos {}^3\left(2\mathrm{x}\right)-\cos \left(\mathrm{x}\right)}{\cos {}^2\left(2\mathrm{x}\right)-\cos \left(\mathrm{x}\right)}=$$ Commented by jagoll last updated on 02/Apr/20 $$\mathrm{i}\:\mathrm{can}\:\mathrm{try} \…

Question Number 152362 by Tawa11 last updated on 27/Aug/21 $$\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}\mathrm{x}\sin \frac{1}{\mathrm{x}},\mathrm{if}0<\mathrm{x}⩽1\\ 0,\mathrm{if}\mathrm{x}=0\end{array}$$$$\mathrm{Show}\mathrm{that}\mathrm{f}\mathrm{is}\mathrm{continous}\mathrm{but}\mathrm{not}\mathrm{of}\mathrm{bounded}\mathrm{variation}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 21223 by moadakennaf last updated on 16/Sep/17 $$\underset{x\to \pi /2}{\lim }(\pi -2x)\tan \left(x\right)$$ Answered by dioph last updated on 16/Sep/17 $$=\underset{x\to \pi /2}{\lim }\frac{\pi -2x}{\cot x}=$$$$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{−\mathrm{2}}{−\mathrm{cosec}^{\mathrm{2}}…