Category: Limits

Question Number 34694 by math khazana by abdo last updated on 09/May/18 $$find{lim}_{n\to +\mathrm{\infty }}\sum _{k=n}^{2n-1}\frac{1}{2k+1}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 100134 by bemath last updated on 25/Jun/20 $$\underset{x\to \frac{\pi }{2}}{\lim }\frac{4\sin \mathrm{x}-\sqrt{6\sqrt{\sin \mathrm{x}}+10}}{\frac{\pi }{2}-\mathrm{x}}?$$ Commented by bobhans last updated on 25/Jun/20 $$\mathrm{set}\frac{\pi }{2}-\mathrm{x}=\mathrm{t},\mathrm{x}=\frac{\pi }{2}-\mathrm{t}$$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4cos}\:\mathrm{t}−\sqrt{\mathrm{6}\sqrt{\mathrm{cos}\:\mathrm{t}}+\mathrm{10}}}{\mathrm{t}}\:= \…

Question Number 34540 by rahul 19 last updated on 07/May/18 $$a)\underset{x\to \frac{\pi }{4}}{\lim }\frac{{(\cos x+\sin x)}^3-2\sqrt{2}}{1-\sin 2x}=?$$$$b)\underset{x\to 0}{\lim }{\left(\sin x\right)}^{\frac{1}{x}}=?$$ Commented by abdo mathsup 649 cc…

Question Number 34516 by rahul 19 last updated on 07/May/18 $$\underset{x\to 0}{\lim }\log {}_{\tan {}^{2}x}\left(\tan {}^{2}2x\right)=?$$ Commented by math khazana by abdo last updated…

Question Number 100037 by bobhans last updated on 24/Jun/20 $$\underset{x\to \mathrm{\infty }}{\lim }\mathrm{x}\sqrt{\mathrm{x}}\sin \left(2\mathrm{x}\right)?$$ Commented by bramlex last updated on 24/Jun/20 $$\underset{x\to \mathrm{\infty }}{\lim }x\sqrt{x}=\mathrm{\infty }\wedge -1⩽\sin 2x⩽1$$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{x}\sqrt{{x}}\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\infty\:…