Question

Сделайте с пошаговым решением, пожалуйста.

Answer 1

$1. lim_{x to 1} frac{x^2 - 2x + 1}{2x^2 - x - 1} = lim_{x to 1} frac{(x-1)^2}{(x-1)(2x+1)} = lim_{x to 1} frac{x-1}{2x+1} = 0$
2.
$lim_{x to 0} frac{ sqrt{1 - 2x + x^2}-(1-x) }{x} = lim_{x to 0} frac{ sqrt{(x-1)^2}+(x-1) }{x}$
$lim_{x to 0} frac{ sqrt{(x-1)^2}+(x-1) }{x} = lim_{x to 0} frac{|x-1| + x -1}{x} = lim_{x to 0} frac{1-x + x -1}{x} = 0$
3.
$lim_{x to -1} frac{x^2 - 4x - 5}{x^2 - 2x -3} = lim_{x to -1} frac{(x-5)(x+1)}{(x-3)(x+1)} = lim_{x to -1} frac{(x-5)}{(x-3)} = frac{6}{4} = frac{3}{2}$