Question

lim x->1. (x^4-x^3-2*x+2)/(x^2-3*x+2)

Answer 1

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