Category: Limits

Question Number 109861 by john santu last updated on 26/Aug/20 $$\frac{JS}{\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◼"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fc.svg">}★★\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◼"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fc.svg">}}$$$$\underset{x\to 3}{\lim }\frac{5-2x+\sqrt{x-2}}{x-4+\sqrt{x-2}}?$$ Answered by bemath last updated on 26/Aug/20 Commented by…

Question Number 109769 by Karani last updated on 25/Aug/20 $$\underset{x\to \mathrm{\Pi }}{\lim }\frac{1-\cos x\cos 2x\cos 3x}{1-\cos x}=?$$ Answered by bemath last updated on 25/Aug/20 $$△\frac{\mathrm{♭}ϵ}{math}▽$$$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\pi.\mathrm{cos}\:\mathrm{2}\pi.\mathrm{cos}\:\mathrm{3}\pi}{\mathrm{1}−\mathrm{cos}\:\pi}\:=\:\frac{\mathrm{1}−\left(−\mathrm{1}\right)\left(\mathrm{1}\right)\left(−\mathrm{1}\right)}{\mathrm{2}}=\mathrm{0} \…

Question Number 109765 by Karani last updated on 25/Aug/20 $$\left(x_n\right)=\frac{{(-1)}^{n}n+10}{\sqrt{n^2+1}},n\in N\mathrm{show}\mathrm{if}\mathrm{the}\mathrm{sequence}\mathrm{is}\mathrm{limited}.$$ Answered by mathmax by abdo last updated on 25/Aug/20 $$\mid\mathrm{x}_{\mathrm{n}}…

Question Number 109733 by bobhans last updated on 25/Aug/20 $$\underset{x\to 0}{\lim }\frac{x-\tan x}{\sin x-x}?$$ Answered by Dwaipayan Shikari last updated on 25/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{3}}}{{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}−{x}}=\mathrm{2}…

Question Number 109722 by bemath last updated on 25/Aug/20 $$⊸\frac{\mathrm{♭}ϵ}{math}⊸$$$$\underset{x\to 0}{\lim }\frac{\sin x}{\sqrt{1-\cos x}}=?$$ Commented by bemath last updated on 25/Aug/20 Answered by mathmax…