Question

Помогите с lim(3-5)^4 - (2-n)^4)/(1-n)^3 - (1+n)^3

Answer 1

$lim_{n->\infty}\dfrac{(3-n-2+n)(3-n+2-n)((3-n)^2+(2-n)^2)}{(1-n-1-n)((1-n)^2+(1-n)(1+n)+(1+n)^2)}=\\ lim_{n->\infty} \dfrac{(5-2n)(13-10n+2n^2)}{(-2n)(2+2n^2+(1-n^2)}=lim_{n->\infty} \dfrac{(5-2n)(13-10n+2n^2)}{(-2n)(3+n^2)}=\\ lim_{n->\infty} \dfrac{(\dfrac{5}{n}-2)(\dfrac{13}{n^2}-\dfrac{10}{n}+2)}{(-2)(\dfrac{3}{n^2}+1)}=\dfrac{-2\cdot 2}{-2\cdot 1}=2$