Category: Limits

Question Number 4281 by Filup last updated on 07/Jan/16 $$\mathrm{The}\mathrm{following}\mathrm{image}\mathrm{shows}\mathrm{the}\mathrm{functiond}$$$$f\left(x\right)={xe}^{\frac{1}{1-x}}\mathrm{and}g\left(x\right)=x-1$$$$$$$$\mathrm{Can}\mathrm{you}\mathrm{explain}\mathrm{as}\mathrm{to}\mathrm{why}\mathrm{as}\mid f\left(x\right)\mid \to \mathrm{\infty },$$$$\mathrm{that}f\left(x\right)\to g\left(x\right).$$ Commented by Filup last…

Question Number 69709 by ahmadshahhimat775@gmail.com last updated on 26/Sep/19 Commented by kaivan.ahmadi last updated on 26/Sep/19 $${lim}_{x\to \mathrm{\infty }}\frac{2x}{3^{x}ln3}={lim}_{x\to \mathrm{\infty }}\frac{2}{3^x{\left(ln3\right)}^2}=0$$ Commented…

Question Number 69667 by ahmadshahhimat775@gmail.com last updated on 26/Sep/19 Answered by Kunal12588 last updated on 26/Sep/19 $$\underset{x\to \frac{\pi }{3}}{lim}\frac{secx-2}{\frac{\pi }{3}-x}$$$$=\underset{x\to \frac{\pi }{3}}{lim}\frac{secxtanx}{-1}$$$$=-2\times \sqrt{3}=-2\sqrt{3}$$…

Question Number 135190 by liberty last updated on 11/Mar/21 $$\underset{x\to 0}{\lim }\frac{1}{{\mathrm{x}}^2}{\int }_0^{\mathrm{x}}\frac{{\mathrm{t}}^2}{{\mathrm{t}}^4+1}\mathrm{dt}?$$$$$$ Answered by metamorfose last updated…

Question Number 69593 by ahmadshahhimat775@gmail.com last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $$letf\left(x\right)=\frac{\sqrt{6-x}-2}{3-\sqrt{11-x}}\Rightarrow$$$${lim}_{x\to 2}f\left(x\right)={lim}_{x\to 2}\frac{(\sqrt{6-x}-2)(\sqrt{6-x}+2)(3+\sqrt{11-x})}{(3-\sqrt{11-x})(3+\sqrt{11-x})(\sqrt{6-x}+2)}$$$$={lim}_{{x}\rightarrow\mathrm{2}}…