Question

calcular o limite quando x tende para -1 de [( raiz quadrada de 3-x) -2] : (x^2 - 1)

Answer 1

$\displaystyle \lim_{x \to -1} \frac{\sqrt{3-x}-2}{x^2-1} = \lim_{x \to -1} \frac{\sqrt{3-x}-2}{x^2-1} . \frac{\sqrt{3-x}+2}{\sqrt{3-x}+2} = \lim_{x \to -1} \frac{(\sqrt{3-x})^2-4}{x^2\sqrt{3-x}+2x^2-\sqrt{3-x}-2}=\\\\ \lim_{x \to -1} -\frac{1}{(\sqrt{-x+3}+2)(x-1)} = -\frac{1}{(\sqrt{-(-1)+3}+2)(-1-1)}=-\frac{1}{(\sqrt{4}+2)(-2)}=-\frac{1}{4(-2)}=\frac{1}{8}$