Question

Qual o limite de (1/x - 1/2)/ (x-2) quando x--> 2 ?

Answer 1

$\\ \lim_{x \to \22} (\frac{1}{x} - \frac{1}{2})/x-2 \\ \lim_{x \to \22} (\frac{1*2 - 1*x}{2x})/x-2 \\ \lim_{x \to \22} ( \frac{2-x}{2x} )/x-2 \\ \lim_{n \to \22} ( \frac{2-x}{2x})*( \frac{1}{x-2)} ) \\ \lim_{x \to \22} -1( \frac{x-2}{2x})*( \frac{1}{x-2} ) \\ \lim_{x \to \22} -1* (\frac{1}{2x} )*( \frac{1}{1} ) \\ \lim_{x \to \22} \frac{-1}{2x} \\ \lim_{x \to \22} \frac{-1}{2*2} \\ \\ \lim_{x \to \22} \frac{-1}{4} = \frac{-1}{4}$