求极限!lim(x→3)sin(x-3)/(x^2-x-6)

问题描述:

求极限!lim(x→3)sin(x-3)/(x^2-x-6)

1。lim(x→3) sin(x-3)/(x-x-6) =lim(x→3) cos(x-3)/(2x-1)=1/5。 2。lim(x→3) sin(x-3)/(x-x-6) =lim(x→3) sin(x-3)/(x-3) ×lim(x→3) 1/(x+2)=1/5。

利用洛必达法则,im(x→3)sin(x-3)/(x^2-x-6)=lim(x→3)cos(x-3)/(2x-1) 带入x=3后等于0.2