Category: Limits

Question Number 28876 by Rasheed.Sindhi last updated on 31/Jan/18 $$\mathcal{E}valuate$$$$\left(\mathrm{i}\right)\underset{x\to -\mathrm{\infty }}{lim}\frac{2-3\mathrm{x}}{\sqrt{3+{4\mathrm{x}}^2}}$$$$\left(\mathrm{ii}\right)\underset{x\to +\mathrm{\infty }}{lim}\frac{2-3\mathrm{x}}{\sqrt{3+{4\mathrm{x}}^2}}$$ Commented by abdo imad last…

Question Number 159936 by qaz last updated on 22/Nov/21 $$\mathrm{Prove}::\underset{\mathrm{n}\to +\mathrm{\infty }}{\bar{\lim }n}\underset{\mathrm{k}=\mathrm{n}+1}{\sum ^{\mathrm{n}}}\frac{{(-1)}^{\mathrm{k}-1}}{\mathrm{k}}=\frac{1}{2}$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 159906 by qaz last updated on 22/Nov/21 $$\underset{\mathrm{x}\to 0}{\lim }\frac{\underset{\mathrm{n}}{\underbrace{\tan \tan \tan \dots \tan \mathrm{x}}}-\underset{\mathrm{n}}{\underbrace{\sin \sin \sin \dots \sin \mathrm{x}}}}{{\mathrm{x}}^2}=?$$ Answered by kaivan.ahmadi last updated on 24/Nov/21 $$\sim{lim}\frac{\frac{{x}^{\mathrm{3}} }{\mathrm{2}}}{{x}^{\mathrm{2}}…

Question Number 28818 by abdo imad last updated on 30/Jan/18 $$provethat\frac{\pi }{4cos\left(\frac{\pi \alpha }{2}\right)}=\sum _{p=0}^{\mathrm{\infty }}\frac{(2p+1){(-1)}^p}{{(2p+1)}^2-{\alpha }^2}$$$$\alpha \in R-Z.$$ Terms of Service Privacy Policy…

Question Number 159852 by Tawa11 last updated on 21/Nov/21 Answered by tounghoungko last updated on 21/Nov/21 $$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{x+2-5}{x+2}\right)}^x=\underset{x\to \mathrm{\infty }}{\lim }{(1-\frac{1}{\left(\frac{x+2}{5}\right)})}^{-\frac{x+2}{5}.\frac{-5x}{(x+2)}}$$$$\:\:=\:{e}^{\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(−\frac{\mathrm{5}{x}}{{x}+\mathrm{2}}\right)\:} \:=\:{e}^{−\mathrm{5}} \:…