Category: Limits

Question Number 124010 by john_santu last updated on 30/Nov/20 $$\underset{x\to 0^{+}}{\lim }\left(\frac{\sin x+\sqrt{1-\cos 3x}}{\tan \left(x\sqrt{2}\right)}\right)=$$$$\underset{x\to 0^{-}}{\lim }\left(\frac{\sin x+\sqrt{1-\cos 3x}}{\tan \left(x\sqrt{2}\right)}\right)=$$$$\underset{x\to 0}{\lim }\left(\frac{\sin x+\sqrt{1-\cos 3x}}{\tan \left(x\sqrt{2}\right)}\right)=$$ Answered by liberty last…

Question Number 189501 by mathlove last updated on 18/Mar/23 $$\underset{x\to 0}{\lim }\frac{e^{x+2x+3x+4x+\dots ..+nx}-1}{x}=?$$ Answered by mehdee42 last updated on 18/Mar/23 $${hop}\rightarrow{lim}_{{x}\rightarrow\mathrm{0}} \left(\mathrm{1}+\mathrm{2}+…+{n}\right){e}^{{x}+\mathrm{2}{x}+…+{nx}} =\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \…

Question Number 123874 by john_santu last updated on 29/Nov/20 $$\left(1\right)\underset{\theta \to 0}{\lim }\frac{\theta -\sin \theta \cos \theta }{\tan \theta -\theta }$$$$\left(2\right)\underset{x\to 0}{\lim }\frac{\sin 3x-3x+x^2}{\sin x\sin 2x}$$ Answered by liberty last updated on 29/Nov/20 $$\:{solve}\:{this}\:{question}\:…

Question Number 58309 by Smail last updated on 21/Apr/19 $$Provethat$$$$\underset{x\to 0}{lim}\frac{1-cos\left(x\right)cos\left(x/2\right)cos\left(x/3\right)\dots }{x^2}=\frac{{\pi }^2}{12}$$ Commented by maxmathsup by imad last updated on…

Question Number 58247 by tanmay last updated on 20/Apr/19 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{S}_{\mathrm{1}} {S}_{{n}} +{S}_{\mathrm{2}} {S}_{{n}−\mathrm{1}} +{S}_{\mathrm{3}} {S}_{{n}−\mathrm{2}} +…+{S}_{{n}} {S}_{\mathrm{1}} }{{S}_{\mathrm{1}} ^{\mathrm{2}} +{S}_{\mathrm{2}} ^{\mathrm{2}} +…+{S}_{{n}} ^{\mathrm{2}} }…