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Question Number 98119 by bobhans last updated on 11/Jun/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{skew}\:\mathrm{lines}\:\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\:=\:\frac{\mathrm{8}−\mathrm{y}}{\mathrm{1}}\:=\:\frac{\mathrm{z}−\mathrm{3}}{\mathrm{1}}\:\mathrm{and}\: \\ $$$$\frac{\mathrm{x}+\mathrm{3}}{−\mathrm{3}}\:=\:\frac{\mathrm{y}+\mathrm{7}}{\mathrm{2}}\:=\:\frac{\mathrm{z}−\mathrm{6}}{\mathrm{4}}\:. \\ $$ Commented by john santu last updated on 11/Jun/20 $$\mathrm{shortest}\:\mathrm{distance}\:\mathrm{lies}\:\mathrm{along}\:\mathrm{a}\:\mathrm{direction}…
Question Number 32402 by saru53424@gmail.com last updated on 24/Mar/18 $$\int\frac{{x}+\mathrm{2}}{\mathrm{1}−{x}} \\ $$ Commented by abdo imad last updated on 24/Mar/18 $$\int\frac{{x}+\mathrm{2}}{\mathrm{1}−{x}}{dx}\:=−\int\:\frac{{x}+\mathrm{2}}{{x}−\mathrm{1}}{dx}\:=−\:\int\frac{{x}−\mathrm{1}+\mathrm{3}}{{x}−\mathrm{1}}{dx} \\ $$$$=−{x}\:−\mathrm{3}\int\:\frac{{dx}}{{x}−\mathrm{1}}\:=−{x}\:−\mathrm{3}{ln}\mid{x}−\mathrm{1}\mid\:+\lambda\:. \\ $$…
Question Number 97901 by pranesh last updated on 10/Jun/20 Commented by pranesh last updated on 10/Jun/20 $${solve}\:{fast}\:{please} \\ $$ Commented by prakash jain last updated…
Question Number 97353 by john santu last updated on 07/Jun/20 Answered by abdomathmax last updated on 07/Jun/20 $$\left.\mathrm{6}\right)\:\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{arcsin}\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{2arctan}\sqrt{\mathrm{x}}−\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{f}^{'} \left(\mathrm{x}\right)\:=\frac{\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\right)^{'} }{\:\sqrt{\mathrm{1}−\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}+\mathrm{1}}\right)^{\mathrm{2}} }}\:=\frac{\mathrm{2}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \sqrt{\frac{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} −\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 95509 by i jagooll last updated on 25/May/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{plane} \\ $$$$\mathrm{2x}−\mathrm{y}+\mathrm{2z}=\mathrm{1}\:\mathrm{and}\:\mathrm{x}+\mathrm{3y}−\mathrm{2z}\:=\:\mathrm{2} \\ $$ Answered by bobhans last updated on 25/May/20 $$\mathrm{let}\:\beta\:=\:\mathrm{angle}\:\mathrm{the}\:\mathrm{plane}\: \\ $$$$\mathrm{cos}\:\beta\:=\:\frac{\mid\mathrm{2}.\mathrm{1}+\left(−\mathrm{1}\right).\mathrm{3}+\mathrm{2}.\left(−\mathrm{2}\right)\mid}{\:\sqrt{\mathrm{9}}\:\sqrt{\mathrm{14}}}\:=\:\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{14}}}…
Question Number 92143 by hore last updated on 05/May/20 $${fond}\int\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by Prithwish Sen 1 last updated on 05/May/20 $$\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\:+\mathrm{c}\:\:\:\mathrm{c}=\:\mathrm{const}. \\…
Question Number 92138 by hore last updated on 05/May/20 $$\int\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$ Answered by john santu last updated on 05/May/20 $$\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\:+\:\mathrm{c}\: \\ $$…
Question Number 26290 by d.monhbayr@gmail.com last updated on 23/Dec/17 $${f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}\: \\ $$$${x}_{\mathrm{0}} =\mathrm{2} \\ $$ Commented by prakash jain last updated on 23/Dec/17 $${what}\:{is}\:{the}\:{questin}…
Question Number 152771 by Tawa11 last updated on 01/Sep/21 $$\mathrm{If}\:\:\:\:\mathrm{f}\left(\mathrm{z}\right)\:\:\:=\:\:\:\:\mathrm{z}\:\mathrm{sin}\left(\mathrm{z}\right)\:\:\:+\:\:\:\mid\mathrm{z}\mid^{\mathrm{2}} ,\:\:\:\:\:\:\:\mathrm{verify}\:\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{z}\right)\:\:\:\mathrm{satisfy}\:\mathrm{cauchy}\:\mathrm{rieman} \\ $$$$\mathrm{condition} \\ $$ Commented by alisiao last updated on 01/Sep/21 $${f}\left({z}\right)=\:{z}\:{sin}\left({z}\right)\:+\:{z}\:\overset{\_} {{z}} \\…