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Question Number 81027 by abdomathmax last updated on 09/Feb/20
$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{tan}\left(\mathrm{2}{x}\right)−\mathrm{2}{tanx}−\mathrm{2}{tan}^{\mathrm{3}} {x}}{{x}^{\mathrm{5}} } \\ $$
Commented by john santu last updated on 09/Feb/20
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{tan2}{x}\:}{\mathrm{2}{x}}.\left(\mathrm{2}{x}\right)−\frac{\mathrm{2tan}\:{x}}{{x}}.\left({x}\right)−\frac{\mathrm{2tan}^{\mathrm{3}} {x}\:}{{x}^{\mathrm{3}} }.\left({x}^{\mathrm{3}} \right)}{{x}^{\mathrm{5}} }\:= \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{x}−\mathrm{2}{x}−\mathrm{2}{x}^{\mathrm{3}} }{{x}^{\mathrm{5}} \:}\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−\mathrm{2}}{{x}^{\mathrm{2}} }\:=\:−\infty \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{−\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:−\infty,\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{−\mathrm{1}}{{x}^{\mathrm{2}} }\:=\:−\infty \\ $$
Commented by john santu last updated on 09/Feb/20
Commented by mathocean1 last updated on 09/Feb/20
$$\mathrm{please}\:\mathrm{which}\:\mathrm{Application}\:\mathrm{do}\:\mathrm{you}\:\mathrm{use}\:\mathrm{to} \\ $$$$\mathrm{make}\:\mathrm{this}\:\mathrm{graphic}\:\mathrm{sir}? \\ $$
Commented by john santu last updated on 09/Feb/20
$${Desmos}\:{graphic}\:{sir} \\ $$
Commented by abdomathmax last updated on 09/Feb/20
$${not}\:{correct}\:{answer}\:{sir}\:{john}...! \\ $$
Commented by john santu last updated on 09/Feb/20
$${give}\:{your}\:{reason}\:{sir}\:! \\ $$