Category: Limits

Question Number 188251 by Rupesh123 last updated on 27/Feb/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 122623 by Ar Brandon last updated on 18/Nov/20 $$\mathrm{Find}\mathrm{the}\mathrm{limits}\mathrm{at}(0,0)\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{functions}:$$$$1.f(\mathrm{x},\mathrm{y})=\frac{{\mathrm{x}}^2{\mathrm{y}}^2}{{\mathrm{x}}^2+{\mathrm{y}}^2}2.f(\mathrm{x},\mathrm{y})=\frac{\mathrm{xy}}{{\mathrm{x}}^2+{\mathrm{y}}^2}3.f(\mathrm{x},\mathrm{y})=\frac{\mathrm{xy}}{\mathrm{x}+\mathrm{y}}$$$$\mathrm{4}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:\:\:\:\:\:\mathrm{5}.\:{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{3x}^{\mathrm{2}}…

Question Number 122550 by liberty last updated on 18/Nov/20 $$\underset{x\to 1/2}{\lim }\frac{{2\mathrm{x}}^2+\mathrm{x}-1}{\tan \left(\pi \mathrm{x}\right)}?$$ Answered by bramlexs22 last updated on 18/Nov/20 $$\underset{x\to 1/2}{\lim }\frac{(2x-1)(x+1)}{\tan \left(\pi x\right)}=$$$$\:\frac{\mathrm{3}}{\mathrm{2}}×\:\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}}…

Question Number 188060 by mathlove last updated on 25/Feb/23 Answered by aleks041103 last updated on 26/Feb/23 $$\underset{x\to 0}{lim}{\left(\underset{k=2}{\prod ^n}\sqrt[k]{cos\left(kx\right)}\right)}^{1/x^2}=$$$$=\underset{{x}\rightarrow\mathrm{0}} {{lim}}\left(\underset{{k}=\mathrm{2}}…

Question Number 122458 by benjo_mathlover last updated on 17/Nov/20 $$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{\sqrt{n}}(\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\dots +\frac{1}{\sqrt{2n-1}+\sqrt{2n+1}})=?$$ Answered by liberty last updated on 17/Nov/20 $$\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}}}\:\left(\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{2k}−\mathrm{1}}+\sqrt{\mathrm{2k}+\mathrm{1}}}\right)\:= \…