Question Number 150560 by DELETED last updated on 13/Aug/21 Answered by DELETED last updated on 13/Aug/21 $$\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{7x}+\mathrm{12}\right)\mathrm{sin}\:\left(\mathrm{x}−\mathrm{3}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{6}\right)^{\mathrm{2}} }\:\:\:\:\:\:\: \\ $$$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\:\left(\mathrm{x}−\mathrm{4}\right)\left(\mathrm{x}−\mathrm{3}\right)\mathrm{sin}\:\left(\mathrm{x}−\mathrm{3}\right)}{\left\{\left(\mathrm{x}+\mathrm{2}\right)\left(\mathrm{x}−\mathrm{3}\right)\right\}^{\mathrm{2}} }…
Question Number 19452 by icyfalcon999 last updated on 11/Aug/17 Answered by Tinkutara last updated on 11/Aug/17 $$\int\frac{{dx}}{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:=\:\mathrm{tan}^{−\mathrm{1}} {x} \\ $$$$\left[\mathrm{tan}^{−\mathrm{1}} {x}\right]_{−\infty} ^{\infty} \:=\:\frac{\pi}{\mathrm{2}}\:−\:\left(−\frac{\pi}{\mathrm{2}}\right)\:=\:\pi \\…
Question Number 150527 by Jamshidbek last updated on 13/Aug/21 $$\sqrt[{\mathrm{3}}]{\mathrm{x}\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}−\mathrm{9}\right)−\mathrm{8}}=\mathrm{2x}+\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} −\mathrm{3x}} \\ $$ Answered by MJS_new last updated on 13/Aug/21 $$\mathrm{trying}\:\mathrm{something}\:\mathrm{weird}: \\ $$$$\mathrm{assuming}\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} −\mathrm{3}{x}}={y}\in\mathbb{R} \\…
Question Number 150508 by saly last updated on 13/Aug/21 Commented by saly last updated on 13/Aug/21 $$\:{Do}\:{you}\:{help}\:{me}? \\ $$ Answered by Olaf_Thorendsen last updated on…
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Question Number 150467 by saly last updated on 12/Aug/21 Commented by saly last updated on 12/Aug/21 $$\:\:{Do}\:{you}\:{help}\:{me} \\ $$ Answered by aleks041103 last updated on…
Question Number 84909 by naka3546 last updated on 17/Mar/20 $${Find}\:\:\:{all}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y}\right)\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} \:−\:\mathrm{3}{xy}^{\mathrm{2}} \:\:=\:\:\mathrm{2010} \\ $$$$\:\:\:\:\:\:\:\:{y}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} {y}\:\:=\:\:\mathrm{2009} \\ $$$${x},\:{y}\:\:\in\:\:\mathbb{R} \\ $$ Commented by john…
Question Number 150432 by Jamshidbek last updated on 12/Aug/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}+\mathrm{1}\right)!}{\mathrm{8}^{\mathrm{n}} \centerdot\left(\mathrm{n}!\right)^{\mathrm{2}} }=?\:\:\:\:\:\mathrm{Help}\:\mathrm{please} \\ $$ Answered by Olaf_Thorendsen last updated on 12/Aug/21 $${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\left(\mathrm{1}−{x}\right)^{\mathrm{3}/\mathrm{2}} }\:=\:\left(\mathrm{1}−{x}\right)^{−\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 150429 by ZiYangLee last updated on 12/Aug/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{tangents}\:\mathrm{to}\:\mathrm{the}\:\mathrm{parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{x}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:{x}^{\mathrm{2}} =\mathrm{2}{y}−\mathrm{3}. \\ $$ Answered by Olaf_Thorendsen last updated on 12/Aug/21…
Question Number 150425 by saly last updated on 12/Aug/21 Commented by saly last updated on 12/Aug/21 $$\:\:\:{Merci}\:\:{beaucoup} \\ $$ Commented by saly last updated on…