Question

me ajudem a calcular o limite: lim  x² - 1
                                              x² + 3x + 2 quando x tende para -1. ta mal alinhado, mas é uma fração

Answer 1

$\underset{x \to -1}{\mathrm{\ell im}}\,\dfrac{x^{2}-1}{x^{2}+3x+2}\\ \\ =\underset{x \to -1}{\mathrm{\ell im}}\,\dfrac{\left(x+1 \right )\left(x-1 \right )}{x^{2}+x+2x+2}\\ \\ =\underset{x \to -1}{\mathrm{\ell im}}\,\dfrac{\left(x+1 \right )\left(x-1 \right )}{x\left(x+1 \right )+2\left(x+1 \right )}\\ \\ =\underset{x \to -1}{\mathrm{\ell im}}\,\dfrac{\left(x+1 \right )\left(x-1 \right )}{\left(x+1 \right )\left(x+2\right)}\\ \\ =\underset{x \to -1}{\mathrm{\ell im}}\,\dfrac{\left(x+1 \right )\left(x-1 \right )}{\left(x+1 \right )\left(x+2\right)}\\ \\ =\underset{x \to -1}{\mathrm{\ell im}}\,\dfrac{x-1}{x+2}\\ \\ =\dfrac{-1-1}{-1+2}\\ \\ =\dfrac{-2}{1}\\ \\ =-2\\ \\ \\ \boxed{\underset{x \to -1}{\mathrm{\ell im}}\,\dfrac{x^{2}-1}{x^{2}+3x+2} =-2}$