Question

lim х стремится к 1 х^4-1/х^3-1

Answer 1

$lim_{x to 1} frac{x^4-1}{x^3-1} =( frac{0}{0} )= lim_{x to 1} frac{(x^2+1)(x+1)(x-1)}{(x-1)(x^2+x+1)}=lim_{x to 1} frac{(x^2+1)(x+1)}{x^2+x+1}=$
$=lim_{x to 1} frac{(1^2+1)(1+1)}{1^2+1+1}=frac{2*2}{3}= frac{4}{3}$
ответ: $frac{4}{3}$