Category: Limits

Question Number 195982 by mathlove last updated on 14/Aug/23 $$\underset{x\to 1}{\lim }[\frac{1}{2(1-\sqrt{x})}-\frac{1}{3(1-\sqrt[3]{x})}]=?$$$$without{l}^{\prime }pitalrule$$ Answered by MM42 last updated on 14/Aug/23 $${lim}_{{x}\rightarrow\mathrm{1}} \:\left(\frac{\mathrm{1}+\sqrt{{x}}}{\mathrm{2}\left(\mathrm{1}−{x}\right)}−\frac{\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} }}{\mathrm{3}\left(\mathrm{1}−{x}\right)}\right)…

Question Number 195905 by cortano12 last updated on 13/Aug/23 $$\underset{x\to 0}{\lim }\frac{\sqrt{3+{\mathrm{x}}^4}-\sqrt{3+\tan {}^4\mathrm{x}}}{{\mathrm{x}}^6}=?$$ Answered by qaz last updated on 13/Aug/23 $$ \…

Question Number 195772 by dimentri last updated on 10/Aug/23 $$\cancel{\underset{―}{\underbrace{}}}\cancel{}$$ Answered by MM42 last updated on 10/Aug/23 $${lim}_{x\to \frac{\pi }{3}}\frac{cos\frac{3x}{2}-2cos\frac{3x}{2}\times sin\frac{3x}{2}}{4cos\frac{3x}{2}sin\frac{3x}{2}cos3x}$$$$={lim}_{{x}\rightarrow\frac{\pi}{\mathrm{3}}}…

Question Number 195618 by cortano12 last updated on 06/Aug/23 $$\cancel{\underset{―}{\underbrace{}}}$$ Answered by MM42 last updated on 06/Aug/23 $$0$$ Commented by…

Question Number 195401 by mnjuly1970 last updated on 01/Aug/23 $$$$$$$$$$\mathrm{calc}\underset{\underset{\Downarrow }{\Downarrow }}{\mathrm{u}late}$$$$$$$${\lim }_{\mathrm{x}\to \frac{\pi }{2}}{\left(\sin \left(\mathrm{x}\right)\right)}^{{\tan }^2\left(\mathrm{x}\right)}=?\overline{)\begin{array}{c}\\ \end{array}}$$$$…