Задача

[Гост]

[tex]\lim_{x \to 4}1-x+\sqrt{5+x}/x-4[/tex]

[S.B.]

[tex]\lim_{x \to 4}1-x+\sqrt{5+x}/x-4[/tex]

[tex]\lim_{x \to 4}\frac{1 - x +\sqrt{5 + x}}{x - 4}[/tex] =

$= \lim_{x \to 4}\frac{[(1 - x) + \sqrt{5 + x}][(1 - x) - \sqrt{x + 5}]}{(x - 4)[(1 - x) - \sqrt{5 + x}]} = $

$= \lim_{x \to 4}\frac{(1 - x)^{2} - (x + 5)}{(x - 4)[(x - 1) - \sqrt{5 +x}]} = $

$= \lim_{x \to 4}\frac{1 -2x + x^{2} - x - 5}{(x - 4)[1 - x - \sqrt{5 + x}} = $

$= \lim_{x \to 4}\frac{x^{2} - 3x - 4}{(x - 4)(1 - x - \sqrt{5 + x})} = $

$= \lim_{x \to 4}\frac{(x + 1)(x - 4)}{(x - 4)(1- x - \sqrt{5 + x})} = $

$= \lim_{x \to 4}\frac{x+1}{1 - x - |\sqrt{5 +x}|} = - \frac{5}{6}$