Category: Limits

Question Number 143252 by bramlexs22 last updated on 12/Jun/21 $$\underset{x\to 0}{\lim }\frac{8x-6x\sin x+\sin 2x}{x^5}=?$$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$\frac{\mathrm{8}{x}−\mathrm{6}{x}\mathrm{sin}{x}+\mathrm{sin2}{x}}{{x}^{\mathrm{5}} }\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{x}}{{x}^{\mathrm{5}}…

Question Number 12062 by tawa last updated on 10/Apr/17 $$\underset{x\to \mathrm{y}}{\lim }\frac{{\mathrm{x}}^{\mathrm{n}}-{\mathrm{y}}^{\mathrm{n}}}{\mathrm{x}-\mathrm{y}}$$ Answered by ajfour last updated on 11/Apr/17 $$\boldsymbol{{x}}^{\boldsymbol{{n}}} −\boldsymbol{{y}}^{\boldsymbol{{n}}} =\left(\boldsymbol{{x}}−\boldsymbol{{y}}\right)\left(\boldsymbol{{x}}^{\boldsymbol{{n}}−\mathrm{1}}…

Question Number 143064 by EDWIN88 last updated on 09/Jun/21 $$\underset{x\to 0}{\lim }\frac{\sqrt[3]{1+{\mathrm{x}}^2}-\sqrt[4]{1-2\mathrm{x}}}{\mathrm{x}+{\mathrm{x}}^2}=?$$$$\underset{x\to 1}{\lim }\frac{\sqrt[3]{7+{\mathrm{x}}^2}-\sqrt{3+{\mathrm{x}}^2}}{\mathrm{x}-1}=?$$ Answered by bramlexs22 last updated…

Question Number 143013 by Study last updated on 08/Jun/21 $$li\underset{x\to \mathrm{\infty }}{m}\frac{\sqrt[3]{x+1}}{x+1}=?$$ Commented by Study last updated on 08/Jun/21 $$whatisthepractice?$$ Commented by…

Question Number 77442 by aliesam last updated on 06/Jan/20 $$provethat$$$$\underset{x\to \mathrm{\infty }}{lim}(\mid \frac{x^{x^2}{(x+2)}^{{(x+1)}^2}}{{(x+1)}^{2x^2+2x+1}}\mid )=e$$ Answered by aliesam last…