Category: Limits

Question Number 167662 by mathlove last updated on 22/Mar/22 $$\underset{x\to 3}{\lim }\left[\sqrt[4]{log\sqrt[3]{2log\sqrt{x^3+2}}}\right]=?$$ Answered by alephzero last updated on 23/Mar/22 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\sqrt[{\mathrm{4}}]{\mathrm{ln}\:\sqrt[{\mathrm{3}}]{\mathrm{2ln}\:\sqrt{{x}^{\mathrm{3}} +\mathrm{2}}}}\:= \…

Question Number 36563 by bshahid010@gmail.com last updated on 03/Jun/18 Commented by prof Abdo imad last updated on 03/Jun/18 $$letusethechangement\frac{a}{x}=t$$$${lim}_{{x}\rightarrow{a}} \left(\mathrm{2}−\frac{{a}}{{x}}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{2}{a}}\right)} \:={lim}_{{t}\rightarrow\mathrm{1}} \left(\mathrm{2}−{t}\right)^{{tan}\left(\:\frac{\pi}{\mathrm{2}{t}}\right)} \…

Question Number 167617 by mathlove last updated on 21/Mar/22 $$\left(1\right)\underset{x\to 0}{\lim }{\left[tan(\frac{\pi }{4}-x)\right]}^{cotx}=?$$$$\left(2\right)\underset{x\to 0}{\lim }[\frac{1}{\sin x}-\frac{1}{x}]=?$$ Answered by cortano1 last updated on 21/Mar/22 $$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}}…

Question Number 167593 by cortano1 last updated on 20/Mar/22 Answered by qaz last updated on 20/Mar/22 $$\mathrm{A}=\underset{\mathrm{x}\to 0}{\lim }\frac{\sqrt{17-2{(\mathrm{x}+2)}^2}\cdot \sqrt[3]{3{(\mathrm{x}+2)}^3+3}-9}{{\mathrm{x}}^2}$$$$=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt{\mathrm{9}−\mathrm{2x}^{\mathrm{2}} −\mathrm{8x}}\centerdot\sqrt[{\mathrm{3}}]{\mathrm{3x}^{\mathrm{3}}…

Question Number 102034 by Study last updated on 06/Jul/20 $$li\underset{x\to 2}{m}\frac{\sqrt[3]{2x+4}-2}{x^2-x-2}=?$$ Answered by Dwaipayan Shikari last updated on 06/Jul/20 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{2}{x}+\mathrm{4}}−\mathrm{2}}{\mathrm{2}{x}+\mathrm{4}−\mathrm{8}}.\frac{\mathrm{2}{x}−\mathrm{4}}{\left({x}−\mathrm{2}\right)\left({x}+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{3}}\mathrm{8}^{\frac{−\mathrm{2}}{\mathrm{3}}} .\frac{\mathrm{2}}{\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{18}}…