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Question-196072




Question Number 196072 by dimentri last updated on 17/Aug/23
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$$\:\:\:\Subset \\ $$
Answered by cortano12 last updated on 18/Aug/23
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$$\:\:\:\underbrace{\Subset} \\ $$
Answered by jabarsing last updated on 18/Aug/23
⇒^(Hop)  lim_(x→((3π)/2))  ((2+(1+cot^2 x))/(−sin x+(4/3)(1+tan^2 (((4x)/3)))))=(9/7)
$$\overset{{Hop}} {\Rightarrow}\:\underset{{x}\rightarrow\frac{\mathrm{3}\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{2}+\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right)}{−\mathrm{sin}\:{x}+\frac{\mathrm{4}}{\mathrm{3}}\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{4}{x}}{\mathrm{3}}\right)\right)}=\frac{\mathrm{9}}{\mathrm{7}} \\ $$

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