Question

Решите предел пожалуйста Lim(x->2) x^2-4/(sqrt(x+7)-3)

Answer 1

$\lim_{x \to 2} \dfrac{x^2 - 4}{ \sqrt{x+7} - 3 } = \lim_{x \to 2} \dfrac{(x^2 - 4)(\sqrt{x+7} + 3 )}{( \sqrt{x+7} - 3)(\sqrt{x+7} + 3 ) } = \\ \\ = \lim_{x \to 2} \dfrac{(x - 2)(x + 2)(\sqrt{x+7} + 3 )}{x + 7 - 9} = \\ \\ = \lim_{x \to 2} \dfrac{(x - 2)(x + 2)(\sqrt{x+7} + 3 )}{x - 2 } = \\ \\ = \lim_{x \to 2} (x + 2)(\sqrt{x+7} + 3 )} = (2 + 2)( \sqrt{2 + 7} + 3) = \\ \\ = 4 \cdot (3 + 3) = 4 \cdot 6 = 24$