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Author: Tinku Tara

1-oo-1-x-x-2-x-1-dx-

Question Number 203681 by SANOGO last updated on 25/Jan/24 $$\int_{\mathrm{1}} ^{+{oo}} \frac{\mathrm{1}}{{x}\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$ Answered by Frix last updated on 25/Jan/24 $${t}=\frac{\mathrm{2}{x}+\mathrm{1}+\mathrm{2}\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{\:\sqrt{\mathrm{3}}} \\…

Question-203648

Question Number 203648 by yaslm last updated on 24/Jan/24 Answered by Frix last updated on 24/Jan/24 $${w}\left({x}+\frac{{l}}{\mathrm{2}}\right)\left({x}−\frac{{l}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{i}\right)\right)\left({x}−\frac{{l}}{\mathrm{2}}\left(\mathrm{1}+\mathrm{i}\right)\right)=\mathrm{0} \\ $$$${x}=−\frac{{l}}{\mathrm{2}}\vee{x}=\frac{{l}}{\mathrm{2}}\left(\mathrm{1}\pm\mathrm{i}\right) \\ $$ Commented by yaslm last…

lim-x-1-2-x-tan-pix-2-

Question Number 203651 by Davidtim last updated on 24/Jan/24 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\mathrm{2}−{x}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{2}}\right)} =? \\ $$ Answered by Mathspace last updated on 24/Jan/24 $${changement}\:\mathrm{1}−{x}={t}\:{give} \\ $$$${f}\left({x}\right)=\left(\mathrm{2}−{x}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\…