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Question Number 174683 by infinityaction last updated on 08/Aug/22

$$\underset{x\to 0}{\lim }\left[\frac{x^2}{\sin x\tan x}\right]$$$$[\cdot ]greatestintegerfunction$$

Answered by a.lgnaoui last updated on 09/Aug/22

$$$$$$\left[\frac{{\mathrm{x}}^2\cos \mathrm{x}}{{\sin }^2\mathrm{x}}\right]=\cos \mathrm{x}\left[\frac{1}{\frac{{\sin }^2\mathrm{x}}{{\mathrm{x}}^2}}\right]$$$${\lim }_{\mathrm{x}\to 0}\frac{{\mathrm{x}}^2}{\sin \mathrm{x}\tan \mathrm{x}}={\lim }_{\mathrm{x}\to 0}\cos x\times {\lim }_{\mathrm{x}\to 0}\frac{1}{{\left(\frac{\mathrm{sinx}}{\mathrm{x}}\right)}^2}=1$$

Commented by infinityaction last updated on 09/Aug/22

$$no$$

Answered by CElcedricjunior last updated on 09/Aug/22

$$1$$$$$$

Commented by infinityaction last updated on 09/Aug/22

$$noansweris0$$

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