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Category: Limits

lim-x-0-tan-x-sin-x-x-2-x-

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…

lim-x-2-x-2-x-6-1-3-x-2-x-2-

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}}…

lim-x-0-1-1-1-x-1-ln-x-

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}}}…

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

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}}…

lim-x-0-5sin-x-7sin-2x-3sin-3x-tan-x-x-

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}}…

lim-x-1-ax-a-b-3-x-1-3-2-find-a-and-b-without-L-hopital-rule-

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}} \\…