Question

求解答lim[x→∞] 2x^3+x-1/4x^3+x^2+3

Answer 1

lim(x→无穷) (2x^3+x-1)/(4x^3+x^2+3)
分子分母同时除 x^3
=lim(x→无穷) (2+1/x^2-1/x^3)/(4+1/x+3/x^3)
=(2+0-0)/(4+0+0)
=1/2

Answer 2

这题属于七中未定式一种无穷比无穷型极限
一般无穷比无穷型和0/0型我们采用洛必达法则
lim[x→∞] 2x^3+x-1/4x^3+x^2+3
=lim[x→∞]6x²+1/12x²+2x
=lim[x→∞]12x/24x+2
=lim[x→∞]12/24
=1/2