求极限lim x→∞ (2x^2+3x+1)⼀(x^4-x^2)

2024-10-31 15:18:53
有3个网友回答
网友(1):

limx=(2x+1)(x+1)/x^2(x+1)(x-1)=(2x+1)/x^2(x-1)
上下同时除以x^2则分子变为2/x+1/x^2,当x→∞时分子为0,分母不为0则此极限为0

网友(2):

分母的次数比分子大,一定是0

网友(3):

(2x^2+3x+1)/(x^4-x^2)=[(2x+1)(x+1)]/[x^2(x-1)(x+1)]=(2x+1)/[x^2(x-1)]=(2x-2+3)/[x^2(x-1)]=2/(x^2)+3/[x^2(x-1)]
因为x→∞,所以lim x→∞ (2x^2+3x+1)/(x^4-x^2)=0