Category: Limits

Question Number 199597 by mnjuly1970 last updated on 05/Nov/23 $$$$$$\mathrm{calculate}\dots$$$$$$$$\mathrm{Q}:{\lim }_{x\to \frac{\pi }{4}}{(1+sin\left(x\right)-cos\left(x\right))}^{tan\left(2x\right)}=?$$$$\bullet \mathcal{N}ice-\mathcal{M}athematics\bullet$$$$$$ Answered…

Question Number 199467 by Calculusboy last updated on 04/Nov/23 Answered by cortano12 last updated on 04/Nov/23 $$\:\mathrm{4}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{a}−\mathrm{2}\right)\mathrm{x}^{\mathrm{3}} +\left(\mathrm{3}+\mathrm{c}\right)\mathrm{x}^{\mathrm{2}} +\left(\mathrm{b}−\mathrm{3}\right)\mathrm{x}+\mathrm{2}+\mathrm{d}}{\mathrm{x}^{\mathrm{2}} \:\left[\sqrt{\mathrm{1}+\frac{\mathrm{a}}{\mathrm{x}}+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{3}} }+\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{4}} }}\:+\sqrt{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}}−\frac{\mathrm{c}}{\mathrm{x}^{\mathrm{2}} }+\frac{\mathrm{3}}{\mathrm{x}^{\mathrm{3}}…

Question Number 199393 by Calculusboy last updated on 02/Nov/23 Answered by cortano12 last updated on 03/Nov/23 $$\mathrm{A}=\underset{x\to 0}{\lim }\frac{(1+\frac{\mathrm{x}}{2011})(1+\frac{2\mathrm{x}}{2012})(1+\frac{3\mathrm{x}}{2013})-1}{\mathrm{x}}$$$$\mathrm{A}=\frac{1}{2011}+\frac{2}{2012}+\frac{3}{2013}$$ Commented by essaad…

Question Number 198952 by ArifinTanjung last updated on 26/Oct/23 $$\underset{x\to 0}{\lim }\frac{\sin 3\mathrm{x}}{\tan 6\mathrm{x}}=\dots .?$$ Answered by Mathspace last updated on 26/Oct/23 $$lim=\frac{3}{6}=\frac{1}{2}$$$$(sin\left(3x\right)\sim 3xandtan\left(6x\right)\sim 6x)$$…

Question Number 198839 by Guillaume last updated on 24/Oct/23 $$limsin\left(x\right)=?$$$$x\to +\mathrm{\infty }$$ Commented by Frix last updated on 25/Oct/23 $$\mathrm{Does}\mathrm{not}\mathrm{exist}.$$ Terms…