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Category: Relation and Functions

calculate-lim-x-0-2x-ln-1-x-1-x-cosx-

Question Number 42788 by maxmathsup by imad last updated on 02/Sep/18 $${calculate}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{2}{x}}{{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)}\:−{cosx} \\ $$ Commented by maxmathsup by imad last updated on 30/Sep/18 $${we}\:{have}\:\frac{\mathrm{2}{x}}{{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)}\:=\frac{\mathrm{2}{x}}{{ln}\left(\mathrm{1}+{x}\right)−{ln}\left(\mathrm{1}−{x}\right)}\:{but}…

calculate-lim-x-pi-4-sin-2x-sin-x-pi-4-sinx-cosx-

Question Number 42781 by maxmathsup by imad last updated on 02/Sep/18 $${calculate}\:{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\:\frac{{sin}\left(\mathrm{2}{x}\right){sin}\left({x}−\frac{\pi}{\mathrm{4}}\right)}{{sinx}\:−{cosx}} \\ $$ Commented by maxmathsup by imad last updated on 04/Oct/18 $${let}\:{A}\left({x}\right)=\frac{{sin}\left(\mathrm{2}{x}\right){sin}\left({x}−\frac{\pi}{\mathrm{4}}\right)}{{sinx}−{cosx}}\:\:{we}\:{have}\:{A}\left({x}\right)=\frac{{sin}\left(\mathrm{2}{x}\right){sin}\left({x}−\frac{\pi}{\mathrm{4}}\right)}{\:\sqrt{\mathrm{2}}{sin}\left({x}−\frac{\pi}{\mathrm{4}}\right)}…