Question

Calcule os limites
A)lim √x-√1/x-1
x→1
b)lim 9x2-1/3x+1
x→-1/3

Answer 1

$\lim_{x \to 1} \frac{\sqrt{x}-\sqrt1}{x-1}= \lim_{x \to 1} \frac{\sqrt{x}-1}{x-1}= \lim_{x \to 1} \frac{\frac{1}{2\sqrt{x}}}{1}=\frac{\frac{1}{2\sqrt{1}}}{1}=\boxed{\boxed{\frac12}}$

$\lim_{x \to -\frac13} \frac{9x^2-1}{3x+1}= \lim_{x \to -\frac13} \frac{(3x-1)(3x+1)}{3x+1}= \lim_{x \to -\frac13} 3x-1=3(-\frac13)-1$ $=\boxed{-2}$