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Question Number 132007 by abdullahquwatan last updated on 10/Feb/21

Answered by bramlexs22 last updated on 10/Feb/21

$$\underset{x\to 0}{\lim }\frac{\cos 2\mathrm{x}+\sin 3\mathrm{x}(\cos \mathrm{x}-\cos 2\mathrm{x})-\cos \mathrm{x}}{\sin {}^2\mathrm{x}+\cos 2\mathrm{x}-1}$$$$=\underset{x\to 0}{\lim }\frac{(\cos 2\mathrm{x}-\cos \mathrm{x})(1-\sin 3\mathrm{x})}{\cos 2\mathrm{x}-\cos {}^2\mathrm{x}}$$$$=\underset{x\to 0}{\lim }\frac{(2\cos {}^2\mathrm{x}-\cos \mathrm{x}-1)}{{\cos }^2\mathrm{x}-1}\times \underset{x\to 0}{\lim }(1-\sin 3\mathrm{x})$$$$=1\times \underset{x\to 0}{\lim }\frac{(2\cos \mathrm{x}+1)(\cos \mathrm{x}-1)}{(\cos \mathrm{x}+1)(\cos \mathrm{x}-1)}$$$$=\frac{3}{2}$$

Commented by abdullahquwatan last updated on 10/Feb/21

$$\mathrm{thanks}$$

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