Question

求水平渐近线和垂直渐近线6x^2/x^2-4x,我想求他们的水平渐近线和垂直渐近线,请告诉我过程,怎么求得的.

Answer 1

f(x) = 6x^2/(x^2-4x)

定义域：x不等于0,x不等于4.

lim(x->无穷）f(x) = lim(x->无穷）6x^2/(x^2-4x) = lim(x->无穷）6/(1-4/x) = 6/1 = 6,

水平渐近线：y = 6.

lim(x->0)f(x) = lim(x->0)6x^2/(x^2-4x) = lim(x->+0)6x/(x-4) = 0/(-4) = 0,

lim(x->4+)f(x) = lim(x->4+)6x^2/(x^2-4x) = lim(x->4+)6x/(x-4)=+无穷

lim(x->4-)f(x) = lim(x->4-)6x^2/(x^2-4x) = lim(x->4-)6x/(x-4)=-无穷,

垂直渐近线：x = 4.