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Question Number 106388 by bemath last updated on 05/Aug/20

$$\underset{x\to 0}{\lim }\frac{1-\cos 4\mathrm{x}\sin {}^2\mathrm{x}-\cos {}^2\mathrm{x}}{{\mathrm{x}}^4}$$

Answered by bemath last updated on 05/Aug/20

Answered by Dwaipayan Shikari last updated on 05/Aug/20

$$\underset{x\to 0}{\lim }\frac{{sin}^{2}x-cos4{xsin}^{2}x}{x^4}$$$$\underset{x\to 0}{\lim }\frac{{sin}^{2}x(1-cos4x)}{x^4}$$$$\underset{x\to 0}{\lim }\frac{2{sin}^{2}x.{sin}^{2}2x}{x^4}=\frac{2x^2{\left(2x\right)}^2}{x^4}=8(sinx\to x)$$

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