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Question Number 190435 by mustafazaheen last updated on 02/Apr/23

$$$$$$\mathrm{how}\mathrm{is}\mathrm{solution}$$$$\underset{x\to 0}{\lim }\frac{{\mathrm{x}}^{10}\cdot {\sin }^4\mathrm{x}\cdot {\cos }^8\mathrm{x}\cdot {(\mathrm{x}+1)}^3}{{\mathrm{x}}^4+{3\mathrm{x}}^3+{3\mathrm{x}}^2+\mathrm{x}}=?$$$$$$

Answered by JDamian last updated on 02/Apr/23

$$0$$

Commented by mustafazaheen last updated on 03/Apr/23

$$\mathrm{how}\mathrm{is}\mathrm{solution}$$

Answered by mr W last updated on 03/Apr/23

$$=\underset{x\to 0}{\lim }\frac{x^{10}\times {\sin }^{4}x\times {\cos }^{8}x\times {(x+1)}^3}{x(1+3x+3x^2+x^3)}$$$$=\underset{x\to 0}{\lim }\frac{x^9\times {\sin }^{4}x\times {\cos }^{8}x\times {(x+1)}^3}{1+3x+3x^2+x^3}$$$$=\frac{0^9\times 0^4\times 1^8\times 1^3}{1}$$$$=0$$

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