Question

lim 9-x/√x-3 quando x tende a 9

Answer 1

Olá Ana!

$\\ \mathsf{\lim_{x \to 9} \frac{9 - x}{\sqrt{x} - 3} =} \\\\\\ \mathsf{\lim_{x \to 9} \frac{9 - x}{\sqrt{x} - 3} \cdot \frac{\sqrt{x} + 3}{\sqrt{x} + 3} =} \\\\\\ \mathsf{\lim_{x \to 9} \frac{(9 - x)(\sqrt{x} + 3)}{x - 9} =} \\\\\\ \mathsf{\lim_{x \to 9} \frac{(9 - x)(\sqrt{x} + 3)}{- (9 - x)} =} \\\\\\ \mathsf{\lim_{x \to 9} \frac{(\sqrt{x} + 3)}{- 1} =}$

$\\ \mathsf{\lim_{x \to 9} \frac{(\sqrt{x} + 3)}{- 1} =} \\\\\\ \mathsf{\lim_{x \to 9} - (\sqrt{x} + 3) =} \\\\\\ \mathsf{- (\sqrt{9} + 3) =} \\\\ \mathsf{- 3 - 3 =} \\\\ \boxed{\boxed{\mathsf{- 6}}}$