Question Number 82924 by jagoll last updated on 26/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}−\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}}} \\ $$ Commented by jagoll last updated on 26/Feb/20 $$\mathrm{the}\:\mathrm{ans}\::\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Commented…
Question Number 148439 by liberty last updated on 28/Jul/21 $$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{x}+\mathrm{6}}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}−\mathrm{2}}\:=? \\ $$ Answered by dumitrel last updated on 28/Jul/21 $$\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{\sqrt{{x}+\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{{x}+\mathrm{6}}−\mathrm{2}\right)}{{x}−\mathrm{2}}+\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{\mathrm{2}\left(\sqrt{{x}+\mathrm{2}}−\mathrm{2}\right)}{{x}−\mathrm{2}}−\underset{{x}\rightarrow\mathrm{2}} {{lim}}\frac{{x}^{\mathrm{2}}…
Question Number 82887 by M±th+et£s last updated on 25/Feb/20 $${find}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{ln}\left(\mathrm{1}+{cos}\left({x}\right)\right)−{ln}\left(\mathrm{2}\right)}{{x}} \\ $$ Commented by msup trace by abdo last updated on 25/Feb/20…
Question Number 82815 by M±th+et£s last updated on 24/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\:\frac{\mathrm{1}}{\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{\frac{\mathrm{1}}{{ln}\left({x}\right)}} }=? \\ $$ Commented by mathmax by abdo last updated on 24/Feb/20 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{−\frac{\mathrm{1}}{{lnx}}}…
Question Number 82800 by jagoll last updated on 24/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{cos}\:\mathrm{2}{x}}{{x}^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated on 24/Feb/20 $${let}\:{f}\left({x}\right)=\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 148328 by liberty last updated on 27/Jul/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}+\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\:=? \\ $$ Answered by EDWIN88 last updated on 27/Jul/21 Answered by mathmax…
Question Number 148323 by liberty last updated on 27/Jul/21 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5sin}\:\mathrm{x}−\mathrm{7sin}\:\mathrm{2x}+\mathrm{3sin}\:\mathrm{3x}}{\mathrm{tan}\:\mathrm{x}−\mathrm{x}}\:=? \\ $$ Answered by EDWIN88 last updated on 27/Jul/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{5cos}\:{x}−\mathrm{14cos}\:\mathrm{2}{x}+\mathrm{9cos}\:\mathrm{3}{x}}{\mathrm{sec}\:^{\mathrm{2}} {x}−\mathrm{1}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 82761 by TANMAY PANACEA last updated on 24/Feb/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({cosx}\right)^{\frac{\mathrm{1}}{{m}}} −\left({cosx}\right)^{\frac{\mathrm{1}}{{n}}} }{{x}^{\mathrm{2}} }\:\:\left[{where}\:{m}\:{and}\:{n}\:{integer}\right] \\ $$ Commented by mr W last updated on 24/Feb/20…
Question Number 82699 by jagoll last updated on 23/Feb/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{{ax}−{a}+{b}}−\mathrm{3}}{{x}−\mathrm{1}}\:=\:−\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${find}\:{a}\:{and}\:{b}\:{without}\:{L}'{hopital}\:{rule} \\ $$ Commented by john santu last updated on 23/Feb/20 $$\left(\mathrm{1}\right)\:{limit}\:{must}\:{be}\:\frac{\mathrm{0}}{\mathrm{0}} \\…
Question Number 82682 by zainal tanjung last updated on 23/Feb/20 $$\mathrm{Help}\:\mathrm{me}\:\mathrm{please}….!! \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{Lim}}\:\left(\frac{\mathrm{1}}{\mathrm{ex}}\right)^{\mathrm{6x}} =… \\ $$ Commented by john santu last updated on 23/Feb/20…