Category: Limits

Question Number 205727 by mathzup last updated on 28/Mar/24 $$calculate{lim}_{x\to 0}\frac{e^x-cosx}{x^2}$$ Commented by lepuissantcedricjunior last updated on 29/Mar/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\boldsymbol{{e}}^{\boldsymbol{{x}}} −\boldsymbol{{cosx}}}{\boldsymbol{{x}}^{\mathrm{2}}…

Question Number 205448 by mathlove last updated on 21/Mar/24 $$A=\underset{x\to 0}{\lim }\frac{sinx}{x^3}=?$$ Answered by namphamduc last updated on 21/Mar/24 $${A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\left({x}\right)}{{x}^{\mathrm{3}} }=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}\right)}{{x}}.{x}^{\mathrm{4}}…

Question Number 205339 by depressiveshrek last updated on 17/Mar/24 $$\underset{x\to 0}{\lim }\frac{\tan \left(\tan x\right)}{\sin (1-\cos x)}$$ Answered by MM42 last updated on 18/Mar/24 $$={lim}_{x\to 0}\frac{tan\left(x\right)}{sin\left(\frac{1}{2}{x}^2\right)}$$$$={lim}_{{x}\rightarrow\mathrm{0}}…

Question Number 205237 by universe last updated on 13/Mar/24 Answered by Berbere last updated on 13/Mar/24 $$n^2+x^2⩾n^2$$$$\frac{{x}}{\mathrm{1}+{x}}\leqslant\mathrm{1}\Rightarrow\frac{{nx}\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}+{x}\right)\left({n}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)}\leqslant{n}.\mathrm{1}.\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{n}^{\mathrm{2}}…

Question Number 205134 by universe last updated on 09/Mar/24 Answered by pi314 last updated on 09/Mar/24 $$nx=y$$$$\Leftrightarrow{A}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{{n}} \frac{{f}\left(\frac{{y}}{{n}}\right)}{\left(\mathrm{1}+{y}^{\mathrm{2}} \right)}{dy}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{{n}}…