Category: Limits

Question Number 117422 by bemath last updated on 11/Oct/20 $$\underset{x\to 0}{\lim }\frac{3\tan 4\mathrm{x}-4\tan 3\mathrm{x}}{3\sin 4\mathrm{x}-4\sin 3\mathrm{x}}=?$$ Answered by bobhans last updated on 11/Oct/20 $$\underset{x\to 0}{\lim }\frac{3\tan 4\mathrm{x}-4\tan 3\mathrm{x}}{3\sin 4\mathrm{x}-4\sin 3\mathrm{x}}=$$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}\left(\mathrm{4x}+\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{4x}\right)^{\mathrm{3}}…

Question Number 117417 by bobhans last updated on 11/Oct/20 $$\underset{x\to 0^{+}}{\lim }{(\tanh \left(\frac{1}{\mathrm{x}}\right)-\frac{1}{\cosh \left(\frac{1}{\mathrm{x}}\right)})}^{\frac{1}{\mathrm{x}}}=?$$ Answered by Lordose last updated on 11/Oct/20 $$1$$…

Question Number 182836 by mathlove last updated on 15/Dec/22 Answered by floor(10²Eta[1]) last updated on 15/Dec/22 $$\underset{x\to 2}{\lim }\frac{2^{\mathrm{x}}\ln 2+3^{\mathrm{x}}\ln 3+4^{\mathrm{x}}\ln 4}{1+2\mathrm{x}+{3\mathrm{x}}^2+{4\mathrm{x}}^3}=\frac{4\ln 2+9\ln 3+16\ln 4}{1+4+12+32}$$$$=\frac{\mathrm{36ln2}+\mathrm{9ln3}}{\mathrm{49}}…

Question Number 182770 by mathlove last updated on 14/Dec/22 Answered by ARUNG_Brandon_MBU last updated on 14/Dec/22 $$\underset{n\to \mathrm{\infty }}{\lim }\frac{\pi }{n}\underset{k=1}{\sum ^n}\sin \left(\frac{k\pi }{n}\right)=\pi {\int }_0^1\sin \left(\pi x\right)dx=2$$ Terms…

Question Number 117164 by bobhans last updated on 10/Oct/20 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }{\left(\frac{\mathrm{n}+9}{2\mathrm{n}-1}\right)}^{\mathrm{n}}=?$$ Answered by bemath last updated on 10/Oct/20 $$\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{2n}−\mathrm{1}+\mathrm{10}−\mathrm{n}}{\mathrm{2n}−\mathrm{1}}\right)^{\mathrm{n}} = \…