Question

Помогите решить пределы

Answer 1

$\lim_{x \to \ 2} \frac{5}{2x-8}=\frac{5}{2*2-8} =\frac{5}{-4} =-\frac{5}{4}$

$\lim_{x \to \ 0} \frac{3x^2-2x}{2x^2-5x} = \lim_{x \to \ 0} \frac{(3x^2-2x)'}{(2x^2-5x)'} = \lim_{x \to \ 0} \frac{6x-2}{4x-5}=\frac{2}{5}$

$\lim_{x \to \ 0} \frac{x}{\sqrt{5-x} -\sqrt{5+x} } = \lim_{x \to \ 0} \frac{x(\sqrt{5-x}+\sqrt{5+x})  }{(\sqrt{5-x}-\sqrt{5+x})(\sqrt{5-x}+\sqrt{5+x})    }  =$

$= \lim_{x \to \ 0} \frac{x(\sqrt{5-x}+\sqrt{5+x})  }{-2x} =-\frac{\sqrt{5-x} }{2}-\frac{\sqrt{5+x} }{2}  =-\sqrt{5}$