Category: Limits

Question Number 115777 by bemath last updated on 28/Sep/20 $$\underset{x\to 0}{\lim }\frac{\sin x-{\tan }^{-1}x}{x^2\ln (1+x)}$$ Answered by bobhans last updated on 28/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+{Px}^{\mathrm{5}}…

Question Number 181173 by universe last updated on 22/Nov/22 Commented by CElcedricjunior last updated on 22/Nov/22 $$\mathit{a})\mathit{f}\left(\mathit{x}\right)=$$$$\mathit{b})\mathit{f}\left(\mathit{x}\right)=$$$$\mathit{c})\mathit{f}\left(\mathit{x}\right)=\mathit{l}\mathit{o}\mathit{g}\left(\mathit{e}\right)$$ Terms of…

Question Number 115616 by bobhans last updated on 27/Sep/20 $$\underset{x\to 0}{\lim }\frac{\sqrt[8]{256+\tan x}-\sqrt[3]{1+\sin x}-1}{\sqrt[6]{1+\tan x}-1}?$$ Answered by john santu last updated on 27/Sep/20 $$\underset{x\to 0}{\lim }\frac{2\sqrt[8]{1+\frac{\tan x}{256}}-\sqrt[3]{1+\sin x}-1}{\sqrt[6]{1+\tan x}-1}=$$$$\underset{{x}\rightarrow\mathrm{0}}…

Question Number 181104 by cortano1 last updated on 21/Nov/22 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{\ln (1+\frac{4}{\mathrm{x}})}{\pi -\arctan \left(2\mathrm{x}\right)}=?$$ Commented by Frix last updated on 21/Nov/22 $$\mathrm{wrong}.$$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{4}}{{x}}\right)}{\pi−\mathrm{arctan}\:\mathrm{2}{x}}\:=\frac{\mathrm{0}}{\frac{\pi}{\mathrm{2}}}=\mathrm{0} \…

Question Number 115541 by bobhans last updated on 26/Sep/20 $$\underset{x\to a}{\lim }{(2-\frac{x}{a})}^{\tan \left(\frac{\pi x}{2a}\right)}=?$$ Answered by bemath last updated on 26/Sep/20 $$L=\underset{x\to a}{\lim }{(2-\frac{x}{a})}^{\tan \left(\frac{\pi x}{2a}\right)}$$$$\mathrm{ln}\:{L}=\underset{{x}\rightarrow{a}}…