Category: Limits

Question Number 83859 by john santu last updated on 06/Mar/20 $$\underset{x\to 0}{\lim }(\frac{1}{x^2}-\cot {}^{2}x)=?$$ Commented by john santu last updated on 06/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}}…

Question Number 149372 by fotosy2k last updated on 05/Aug/21 Answered by john_santu last updated on 05/Aug/21 $$\underset{x\to 0}{\lim }\frac{\sin (\mathrm{x}+2\sin \mathrm{x})}{\sin \mathrm{x}}=$$$$\underset{x\to 0}{\lim }\frac{\frac{\sin (\mathrm{x}+2\sin \mathrm{x})}{\mathrm{x}+2\sin \mathrm{x}}.\mathrm{x}+2\sin \mathrm{x}}{\frac{\sin \mathrm{x}}{\mathrm{x}}.\mathrm{x}}$$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}+\mathrm{2sin}\:\mathrm{x}}{\mathrm{x}}\:=\:\mathrm{1}+\mathrm{2}=\mathrm{3} \…

Question Number 149346 by Study last updated on 04/Aug/21 $$li\underset{x\to \mathrm{\infty }}{m}{\left(\frac{3x+12}{6x-20}\right)}^{2x}=?$$ Commented by Study last updated on 04/Aug/21 $$helpeme$$ Answered…

Question Number 149251 by john_santu last updated on 04/Aug/21 $$\underset{x\to 0^{+}}{\lim }\frac{\tan \mathrm{x}\sqrt{\tan \mathrm{x}}-\sin \mathrm{x}\sqrt{\sin \mathrm{x}}}{{\mathrm{x}}^3\sqrt{\mathrm{x}}}=?$$$$$$ Answered by dumitrel last updated on 04/Aug/21 $$\underset{{x}\rightarrow\mathrm{0}^{+}…

Question Number 83690 by jagoll last updated on 05/Mar/20 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{\tan \left(\frac{\pi x+1}{2x+2}\right)}{x+1}=?$$ Commented by mathmax by abdo last updated on 05/Mar/20 $$letf\left(x\right)=\frac{tan\left(\frac{\pi x+1}{2x+2}\right)}{x+1}\Rightarrow f\left(x\right)=\frac{tan\left(\frac{\pi }{2}\times \frac{x+\frac{1}{\pi }}{x+1}\right)}{x+1}$$$$=\frac{{tan}\left(\frac{\pi}{\mathrm{2}}×\left(\frac{{x}+\mathrm{1}\:+\frac{\mathrm{1}}{\pi}−\mathrm{1}}{{x}+\mathrm{1}}\right)\right)}{{x}+\mathrm{1}}\:=\frac{{tan}\left(\frac{\pi}{\mathrm{2}}\left(\mathrm{1}+\frac{\mathrm{1}−\pi}{\pi\left({x}+\mathrm{1}\right)}\right)\right.}{{x}+\mathrm{1}}…