Question

Calcule o Lim (√x-1)/(√(2x+3)-√5) quando x->1

Answer 1

$\lim_{x \to 1} \frac{\sqrt{x-1}}{\sqrt{2x-3}-\sqrt{5}} \\ \\ \lim_{x \to 1} \frac{(\sqrt{x-1}) *(\sqrt{2x-3}+\sqrt{5}) }{\sqrt{2x-3}-\sqrt{5}) * (\sqrt{2x-3}+\sqrt{5})} \\ \\lim_{x \to 1} \frac{\sqrt{2x^2 -5x + 3}+\sqrt{5x-5}}{2x - 3 - 5} \\ \\ \frac{\sqrt{2(1)^2 -5(1) + 3}+\sqrt{5(1)-5}}{2(1) -8} \\ \\ \frac{\sqrt{2-5 + 3}+\sqrt{5-5}}{2 -8} \\ \\ \frac{\sqrt{0}+\sqrt{0}}{-6} = 0$