Category: Limits

Question Number 65473 by Tawa1 last updated on 30/Jul/19 Commented by mathmax by abdo last updated on 30/Jul/19 $$letA\left(x\right)=\sqrt{\frac{x^3-1}{x+1}}{-}^3\sqrt{\frac{x^5+1}{x^2-2x}}\Rightarrow forx>0$$$${A}\left({x}\right)\:=\sqrt{\frac{{x}^{\mathrm{3}}…

Question Number 130965 by Hilolaxon last updated on 31/Jan/21 Answered by bramlexs22 last updated on 31/Jan/21 $$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{−{x}^{\mathrm{5}} \left(−\mathrm{8}+\frac{\mathrm{4}}{{x}^{\mathrm{2}} }−\frac{\mathrm{4}}{{x}^{\mathrm{5}} }\right)}{−{x}^{\mathrm{5}} \left(−\frac{\mathrm{2}}{{x}^{\mathrm{2}} }−\frac{\mathrm{1}}{{x}^{\mathrm{4}} }+\frac{\mathrm{7}}{{x}^{\mathrm{5}} }\right)}\:=−\infty\:…

Question Number 130869 by EDWIN88 last updated on 30/Jan/21 $$\underset{x\to 0}{\lim }{\left(\frac{\tan x}{x}\right)}^{\frac{\tan x}{x-\tan x}}?$$ Answered by benjo_mathlover last updated on 30/Jan/21 $$\ln \mathrm{L}=\underset{x\to 0}{\lim }\left(\frac{\tan \mathrm{x}}{\mathrm{x}-\tan \mathrm{x}}\right)\ln \left(\frac{\tan \mathrm{x}}{\mathrm{x}}\right)$$$$\:\mathrm{ln}\:\mathrm{L}=\:\underset{{x}\rightarrow\mathrm{0}}…

Question Number 130854 by mathlove last updated on 29/Jan/21 $$\underset{x\to 2}{\lim }\frac{x^x\cdot x!-4(3x-4)!}{3x!-6}$$ Answered by Dwaipayan Shikari last updated on 29/Jan/21 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{{x}^{{x}} \left(\mathrm{1}+{logx}\right){x}!+{x}^{{x}}…

Question Number 130843 by EDWIN88 last updated on 29/Jan/21 $$Without{L}^{\prime }H\widehat{opital}$$$$\underset{x\to 1}{\lim }\frac{\sqrt[3]{x^3+7}-\sqrt{x^2+3}}{x-1}?$$ Answered by mathmax by abdo last updated…