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Question Number 190253 by 073 last updated on 30/Mar/23

Answered by cortano12 last updated on 30/Mar/23

$$\mathrm{L}=\underset{x\to 0}{\lim }\frac{(\tan \mathrm{x}+\mathrm{x})(\tan \mathrm{x}-\mathrm{x})}{{\mathrm{x}}^2\tan {}^2\mathrm{x}}$$$$\mathrm{L}=\underset{x\to 0}{\lim }\frac{\tan \mathrm{x}+\mathrm{x}}{\mathrm{x}}.\underset{x\to 0}{\lim }\frac{\tan \mathrm{x}-\mathrm{x}}{\mathrm{x}\tan {}^2\mathrm{x}}$$$$\mathrm{L}=2.\underset{x\to 0}{\lim }\frac{\tan \mathrm{x}-\mathrm{x}}{{\mathrm{x}}^3}$$$$\mathrm{L}=\frac{2}{3}$$

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