Category: Limits

Question Number 113601 by bobhans last updated on 14/Sep/20 Answered by bemath last updated on 14/Sep/20 Commented by bobhans last updated on 14/Sep/20 $$\mathrm{santuyy} \…

Question Number 113576 by bemath last updated on 14/Sep/20 $$\underset{r\to \mathrm{\infty }}{\lim }\sqrt{4r^2+2r}-\sqrt[3]{8r^3+4r^2}=?$$ Answered by bemath last updated on 14/Sep/20 $$\Leftrightarrow\:\underset{{r}\rightarrow\infty} {\mathrm{lim}}{r}\left(\sqrt{\mathrm{4}+\frac{\mathrm{2}}{{r}}}−\sqrt[{\mathrm{3}\:}]{\mathrm{8}+\frac{\mathrm{4}}{{r}}}\right)\:=…

Question Number 113438 by bemath last updated on 13/Sep/20 $$\underset{x\to \mathrm{\infty }}{\lim }x(5^{\frac{1}{x}}-1)?$$ Answered by bemath last updated on 13/Sep/20 Answered by JDamian last…

Question Number 113274 by bemath last updated on 12/Sep/20 $$\left(1\right)\underset{x\to 0}{\lim }\frac{\tan \mathrm{x}+4\tan 2\mathrm{x}-3\tan 3\mathrm{x}}{{\mathrm{x}}^2\tan \mathrm{x}}$$$$\left(2\right)\underset{x\to 0}{\lim }\frac{\sqrt{\mathrm{x}}-\sqrt{\sin \mathrm{x}}}{{\mathrm{x}}^{\frac{3}{2}}}$$$$\left(3\right)\underset{x\to 0}{\lim }\frac{\sqrt{\mathrm{x}}+\sqrt{\sin \mathrm{x}}}{{\mathrm{x}}^{\frac{5}{2}}}$$ Commented by bemath…

Question Number 178716 by cortano1 last updated on 20/Oct/22 $$\underset{x\to 0}{\lim }\frac{3\tan 4\mathrm{x}-4\tan 3\mathrm{x}}{3\sin 4\mathrm{x}-4\sin 3\mathrm{x}}=?$$ Answered by a.lgnaoui last updated on 21/Oct/22 $$f\left(x\right)=(\frac{\tan 4\mathrm{x}(3-\frac{4\tan 3\mathrm{x}}{\tan 4\mathrm{x}})}{\sin 4\mathrm{x}(3-\frac{4\sin 3\mathrm{x}}{\sin 4\mathrm{x}})}=\frac{1}{\cos 4\mathrm{x}}\times \left(\frac{3-\frac{4\sin 3\mathrm{x}}{\cos 3\mathrm{x}}\times \frac{\cos 4\mathrm{x}}{\sin 4\mathrm{x}}}{3-\frac{4\sin 3\mathrm{x}}{\sin 4\mathrm{x}}}\right)$$$$\frac{1}{\cos 4\mathrm{x}}\times \left(\frac{3-\frac{4\sin 3\mathrm{x}}{\sin 4\mathrm{x}}\times \frac{\cos 4\mathrm{x}}{\cos 3\mathrm{x}}}{3-\frac{4\sin 3\mathrm{x}}{\sin 4\mathrm{x}}}\right)$$$$\mathrm{x}\rightarrow\mathrm{0}\:\:\:\:\:{f}\left({x}\right)\rightarrow\frac{\mathrm{3}−\frac{\mathrm{4sin}\:\mathrm{3x}}{\mathrm{sin}\:\mathrm{4x}}}{\mathrm{3}−\frac{\mathrm{4sin}\:\mathrm{3x}}{\mathrm{sin}\:\mathrm{4x}}}=\:\:\frac{\mathrm{3}−\mathrm{4}\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{3x}}×\frac{\mathrm{4x}}{\mathrm{sin}\:\mathrm{4x}}}{\mathrm{3}−\mathrm{4}\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{3x}}×\frac{\mathrm{3x}}{\mathrm{sin}\:\mathrm{4x}}}\:\:=\mathrm{1}…