Category: Limits

Question Number 154593 by Niiicooooo last updated on 19/Sep/21 Commented by Niiicooooo last updated on 19/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 19/Sep/21 $${S}=\underset{{n}=\mathrm{1}} {\overset{\infty}…

Question Number 88985 by jagoll last updated on 14/Apr/20 $$\underset{x\to 3}{\lim }\ln \mid x-3\mid$$$$existorno?$$ Commented by mr W last updated on 14/Apr/20 $${no}. \…

Question Number 88896 by M±th+et£s last updated on 13/Apr/20 $$find$$$$\underset{x\to 0}{lim}\frac{ln(sin\left(3x\right)+cos\left(3x\right))}{ln(sin\left(x\right)+cos\left(x\right))}$$ Commented by abdomathmax last updated on 13/Apr/20 $$letf\left(x\right)=\frac{ln(sin\left(3x\right)+cos\left(3x\right))}{ln(sinx+cosx)}wehave$$$${sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\sim\mathrm{3}{x}\:+\mathrm{1}−\frac{\left(\mathrm{3}{x}\right)^{\mathrm{2}}…

Question Number 154390 by liberty last updated on 18/Sep/21 $$\underset{x\to 2}{\lim }\frac{x^2{e}^x-4e^2}{x-2}?$$ Commented by puissant last updated on 18/Sep/21 $$=\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left(\mathrm{2}{xe}^{{x}}…

Question Number 154292 by mnjuly1970 last updated on 16/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 16/Sep/21 $$S=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{n}{3\cdot 5\cdot \cdot \cdot (2n+1)}=\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{n(2\cdot 4\cdot 6\cdot \cdot \cdot 2n)}{2\cdot 3\cdot 4\cdot 5\cdot 6\cdot \cdot \cdot \left(2n\right)(2n+1)}$$$$\:\:\:=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{2}^{{n}}…