Question

АЛГЕБРА 10КЛАСС x-->x0

1) f(x)=2x-x^2 / x-2 ; x-->2
2) f(x)=x^3-27 / x-3 ; x-->3
3) f(x)=3x^2+2x-1 / x+1 ; x-->-1
4) f(x)=x^2-4 / x^4-16 ; x-->2

Answer 1

$1); ; limlimits _{x to 2}frac{2x-x^2}{x-2}=limlimits _{x to 2} frac{x(2-x)}{-(2-x)} = limlimits _{x to 2} (-x)=-2\\2); ; limlimits _{x to 3} frac{x^3-27}{x-3} = limlimits _{x to 3}frac{(x-3)(x^2+3x+9)}{x-3} = limlimits _{x to 3}(x^2+3x+9)=27\\3); ; limlimits _{x to -1}frac{3x^2+2x-1}{x+1}=limlimits _{x to -1}frac{3(x+1)(x-frac{1}{3})}{x+1} = limlimits _{x to -1} (3x-1)=-4\\4); ; limlimits _{x to 2}frac{x^2-4}{x^4-16}=limlimits _{x to 2}frac{x^2-4}{(x^2-4)(x^2+4)}=limlimits _{x to 2}frac{1}{x^2+4}=frac{1}{8}$