Question

Наайти границы функции lim x направленый к 1 ((sqrt5-x)-(sqrt2x+2))/(x^2-4x+3)

Answer 1

$displaystyle lim_{x to1} frac{ sqrt{5-x}- sqrt{2x+2} }{x^2-4x+3} =displaystyle lim_{x to1} frac{5-x-2x-2}{(x-1)(x-3) (sqrt{5-x}+ sqrt{2x+2} ) } =\ \ \ \ =displaystyle lim_{x to1} frac{-3x+3}{(x-1)(x-3)( sqrt{5-x} + sqrt{2x+2} )} =\ \ \ \ =displaystyle lim_{x to1} frac{-3(x-1)}{(x-1)(x-3)( sqrt{5-x} + sqrt{2x+2} )} =\ \ \ \ =displaystyle lim_{x to1} frac{-3}{(x-3)( sqrt{5-x} + sqrt{2x+2} )} = frac{-3}{(1-3)( sqrt{5-1} + sqrt{2cdot1+2}) } = frac{3}{8}$