Category: Limits

Question Number 154652 by EDWIN88 last updated on 20/Sep/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\mathrm{tan}\:\left(\mathrm{2}{x}+\frac{\pi}{\mathrm{4}}\right)\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−\mathrm{3}{x}\right)}{{x}^{\mathrm{3}} }=? \\ $$ Answered by bramlexs22 last updated on 20/Sep/21 Commented by mnjuly1970 last…

Question Number 154593 by Niiicooooo last updated on 19/Sep/21 Commented by Niiicooooo last updated on 19/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 19/Sep/21 $${S}=\underset{{n}=\mathrm{1}} {\overset{\infty}…

Question Number 88985 by jagoll last updated on 14/Apr/20 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\mathrm{ln}\:\mid{x}−\mathrm{3}\mid\: \\ $$$${exist}\:{or}\:{no}? \\ $$ Commented by mr W last updated on 14/Apr/20 $${no}. \\…

Question Number 88896 by M±th+et£s last updated on 13/Apr/20 $${find}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{ln}\left({sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\right)}{{ln}\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)} \\ $$ Commented by abdomathmax last updated on 13/Apr/20 $${let}\:{f}\left({x}\right)=\frac{{ln}\left({sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\right)}{{ln}\left({sinx}+{cosx}\right)}\:\:{we}\:{have} \\ $$$${sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\sim\mathrm{3}{x}\:+\mathrm{1}−\frac{\left(\mathrm{3}{x}\right)^{\mathrm{2}}…

Question Number 154390 by liberty last updated on 18/Sep/21 $$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} {e}^{{x}} −\mathrm{4}{e}^{\mathrm{2}} }{{x}−\mathrm{2}}\:? \\ $$ Commented by puissant last updated on 18/Sep/21 $$=\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left(\mathrm{2}{xe}^{{x}}…