Category: Limits

Question Number 161612 by cortano last updated on 20/Dec/21 $$\underset{x\to 0^{+}}{\lim }\sqrt[x]{\cos \sqrt{x}}=?$$ Answered by Ar Brandon last updated on 20/Dec/21 $${A}=\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\sqrt[{{x}}]{\mathrm{cos}\sqrt{{x}}}=\underset{{x}\rightarrow\mathrm{0}^{+}…

Question Number 161586 by blackmamba last updated on 20/Dec/21 $$\underset{x\to 2^{-}}{\lim }\frac{2-2\cos \sqrt{x-2}}{{(x-2)}^2}=?$$ Commented by cortano last updated on 20/Dec/21 Commented by mathmax…

Question Number 30511 by abdo imad last updated on 22/Feb/18 $$find{lim}_{x\to +\mathrm{\infty }}{e}^x\left[\frac{1}{x}\right].$$ Commented by abdo imad last updated on 24/Feb/18 $${for}\:{x}>\mathrm{1}\:\Rightarrow\:\mathrm{0}<\frac{\mathrm{1}}{{x}}<\mathrm{1}\:\Rightarrow\:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\:\Rightarrow\:\forall{x}>\mathrm{1}\:{e}^{{x}} \:\left[\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\Rightarrow…

Question Number 30510 by abdo imad last updated on 22/Feb/18 $$find{lim}_{x\to 0^{+}}\sqrt{x}\left[\frac{1}{x}\right]and{lim}_{x\to +\mathrm{\infty }}\frac{\left[x\right]}{x}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 30502 by abdo imad last updated on 22/Feb/18 $$find{lim}_{x\to 0}{(sinx+cosx)}^{\frac{1}{x}}.$$ Answered by sma3l2996 last updated on 24/Feb/18 $$\left({sinx}+{cosx}\right)^{\mathrm{1}/{x}} ={e}^{\frac{{ln}\left({sinx}+{cosx}\right)}{{x}}} \…