Question

$lim( \frac{ (\frac{2}{x} - 2 )}{x - 1} )$
lim x tende para 1​

Answer 1

Explicação passo-a-passo:

$lim_{ x - > 1}( \frac{ \frac{2}{x} - 2 }{x - 1} )$

$lim_{x - > 1}( \frac{ \frac{2}{x} - \frac{2x}{x} }{x - 1} )$

$lim_{x - > 1}( \frac{ \frac{2 - 2x}{x} }{x - 1} )$

$lim_{x - > 1}( \frac{2 - 2x}{x} ) ( \frac{1}{x - 1} )$

$lim_{x - > 1}( \frac{2 - 2x}{x(x - 1)} )$

$lim_{x - > 1}( \frac{ - 2( - 1 + x)}{x(x - 1)} )$

$- 2 lim_{x - > 1}( \frac{x - 1}{x(x - 1)} )$

$- 2 lim_{x - > 1}(x)$

$= - 2(1)$

$= - 2$