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Question Number 197029 by cortano12 last updated on 06/Sep/23

$$\underset{x\to 0}{\lim }\frac{{\mathrm{x}}^8-\sin {}^8\mathrm{x}}{{\mathrm{x}}^{10}}=?$$

Answered by MM42 last updated on 06/Sep/23

$${lim}_{x\to 0}\frac{(x^4+{sin}^{4}x)(x^2+{sin}^{2}x)(x+sinx)(x-sinx)}{x^{10}}$$$$={lim}_{x\to 0}\frac{2x^4\times 2x^2\times 2x\times \frac{1}{6}{x}^3}{x^{10}}=\frac{4}{3}✓$$$$$$

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