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Author: Tinku Tara

Question-74235

Question Number 74235 by aliesam last updated on 20/Nov/19 Answered by Joel578 last updated on 20/Nov/19 $$\mid{x}\mid\:=\:\sqrt{{x}^{\mathrm{2}} } \\ $$$${f}\left({x}\right)\:=\:\sqrt{\left({x}^{\mathrm{2}} \:−\:\mathrm{3}\right)^{\mathrm{2}} } \\ $$$${f}\:'\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\left({x}^{\mathrm{2}} \:−\:\mathrm{3}\right)^{\mathrm{2}}…

lim-x-0-1-cos-2x-1-cos-x-

Question Number 139766 by mohammad17 last updated on 01/May/21 $${lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\sqrt{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}}{\mathrm{1}−{cos}\left({x}\right)}\right) \\ $$ Answered by bramlexs22 last updated on 01/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\left(\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}\right)}}{\mathrm{1}−\mathrm{cos}\:\mathrm{x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}}…

0-x-ln-x-dx-

Question Number 8691 by FilupSmith last updated on 22/Oct/16 $$\int_{\mathrm{0}} ^{\:\infty} {x}^{−\mathrm{ln}\left({x}\right)} {dx} \\ $$ Commented by FilupSmith last updated on 22/Oct/16 $${x}^{−\mathrm{ln}\left({x}\right)} ={e}^{−\mathrm{ln}\left({x}\right)\mathrm{ln}\left({x}\right)} ={e}^{−\mathrm{ln}^{\mathrm{2}}…