0
这个题要用洛必达法则,上下求导,需要知道cos3x等价无穷小是多少,x^3求导是3星^2,再看题目是趋向于∞还是0,再进行下一步计算
cos3x除以x三次方的极限
(x→0)lim{(1-cosx)/x³}
= (x→0)lim{[1-1+2sin²(x/2)]/x³}
= (x→0)lim{2sin²(x/2)]/8*(x/2)³}
= (x→0)lim{sin²(x/2)]/4*(x/2)³}
= (x→0)lim{(x/2)²]/4*(x/2)³}
= +∞
(x→0)lim{(1-cosx)/x³}
= (x→0)lim{[1-1+2sin²(x/2)]/x³}
= (x→0)lim{2sin²(x/2)]/8*(x/2)³}
= (x→0)lim{sin²(x/2)]/4*(x/2)³}
= (x→0)lim{(x/2)²]/4*(x/2)³}
= +∞
(x→0)lim{(1-cosx)/x³}
= (x→0)lim{[1-1+2sin²(x/2)]/x³}
= (x→0)lim{2sin²(x/2)]/8*(x/2)³}
= (x→0)lim{sin²(x/2)]/4*(x/2)³}
= (x→0)lim{(x/2)²]/4*(x/2)³}
= +∞