Category: Limits

Question Number 120823 by bramlexs22 last updated on 03/Nov/20 Answered by liberty last updated on 03/Nov/20 $$\rho =\underset{x\to 0}{\lim }\frac{\sqrt{\cos \mathrm{x}+\sqrt{2\sin {}^2\mathrm{x}+{\mathrm{x}}^3}}-1}{\mathrm{xsin}\mathrm{x}}$$$$\:\rho=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{x}−\mathrm{1}\right)+\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{x}^{\mathrm{3}} }}{\mathrm{x}\:\mathrm{sin}\:\mathrm{x}}\:.\left(\frac{\mathrm{1}}{\mathrm{2}}\right)…

Question Number 186267 by TUN last updated on 02/Feb/23 $$\underset{x\to 0}{\lim }\frac{{(1+2016x)}^{2017}-{(1+2017x)}^{2016}}{x^2}$$$$without{L}^{\prime }Horseries$$ Commented by JDamian last updated on 02/Feb/23…

Question Number 120686 by bobhans last updated on 01/Nov/20 $$\underset{x\to 0}{\lim }\frac{\sin \mathrm{x}-\tan \mathrm{x}}{{\mathrm{x}}^3}?$$ Answered by john santu last updated on 02/Nov/20 $$standartway$$$$\:\underset{{x}\rightarrow\mathrm{0}}…

Question Number 186065 by TUN last updated on 31/Jan/23 $$\underset{x\to 1}{\lim }\frac{\sqrt[3]{x^3+7x^2+10x+9}-\sqrt{6x+3}}{{(x-1)}^2}$$$$$$ Commented by Frix last updated on 01/Feb/23…

Question Number 186066 by TUN last updated on 31/Jan/23 $$\underset{x\to \mathrm{\infty }}{\lim }x(\sqrt{4x^2-12x+7}-\sqrt{x^2-4x-2}-x+1)$$$$\underset{x\to \mathrm{\infty }}{\lim }(\sqrt{x^2+3x}-\sqrt[3]{x^3+2x^2})$$$$$$ Answered by…