Question

lim de x³+x² / 3x³+x⁴+x quando X tende a 0

Answer 1

$\underset{x \to 0}{\mathrm{\ell im}}\;\dfrac{x^{3}+x^{2}}{x^{4}+3x^{3}+x}\\ \\ =\underset{x \to 0}{\mathrm{\ell im}}\;\dfrac{x^{2} \cdot \left(x+1 \right )}{x\cdot \left(x^{3}+3x^{2}+1 \right )}\\ \\ =\underset{x \to 0}{\mathrm{\ell im}}\;\dfrac{x \cdot \left(x+1 \right )}{x^{3}+3x^{2}+1}\\ \\ =\dfrac{0 \cdot \left(0+1 \right )}{0^{3}+3\cdot 0^{2}+1}\\ \\ =\dfrac{0 \cdot 1}{0+0+1}\\ \\ =\dfrac{0}{1}\\ \\ =0\\ \\ \\ \boxed{\underset{x \to 0}{\mathrm{\ell im}}\;\dfrac{x^{3}+x^{2}}{x^{4}+3x^{3}+x}=0}$