Category: Limits

Question Number 85061 by M±th+et£s last updated on 18/Mar/20 $$\underset{x\to 0}{lim}\frac{xtan2x-2xtan\left(x\right)}{{(1-cos\left(2x\right))}^2}$$ Commented by mathmax by abdo last updated on 18/Mar/20 $${let}\:{f}\left({x}\right)=\frac{{xtan}\left(\mathrm{2}{x}\right)−\mathrm{2}{x}\:{tan}\left({x}\right)}{\left(\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)\right)^{\mathrm{2}} }\:\:{we}\:{have}\:…

Question Number 150567 by DELETED last updated on 13/Aug/21 Answered by DELETED last updated on 13/Aug/21 $$\left.\mathrm{1}\right).\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{4}}{\mathrm{2x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\:=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3x}^{\mathrm{2}} /\mathrm{x}^{\mathrm{2}} −\mathrm{4}/\mathrm{x}^{\mathrm{2}} }{\mathrm{2x}^{\mathrm{2}} /\mathrm{x}^{\mathrm{2}}…

Question Number 84932 by jagoll last updated on 17/Mar/20 $$\underset{x\to 0}{\lim }\frac{\sin 38\mathrm{x}-38\sin \mathrm{x}}{{19\mathrm{x}}^3}=$$ Commented by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{38cos}\:\mathrm{38x}\:−\:\mathrm{38cos}\:\mathrm{x}}{\mathrm{3}.\mathrm{19x}^{\mathrm{2}} }\:=…

Question Number 84873 by john santu last updated on 17/Mar/20 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{{\mathrm{x}}^2\sin \left(\frac{\mathrm{x}!}{\mathrm{x}}\right)}{{\mathrm{x}}^2+1}$$ Commented by john santu last updated on 17/Mar/20 $$\mathrm{yes}.\:\mathrm{i}\:\mathrm{agree}\:\mathrm{sir}…

Question Number 19271 by Joel577 last updated on 08/Aug/17 $$\underset{x\to \pi }{\lim }{(2-{\cos }^{2}x)}^{\frac{2\sqrt{2(1+\cos x)}}{{(x-\pi )}^3}}$$ Answered by ajfour last updated on 09/Aug/17 $$=\underset{{x}\rightarrow\pi} {\mathrm{lim}}\left\{\left[\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \left(\pi−\mathrm{x}\right)\right]^{\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}}…