Question

求 x^2/（1-cosx） 当x趋向于0时的极限,看答案好多不懂,

Answer 1

lim[x→0] x²/(1-cosx) 注：1-cosx等价于(1/2)x²
=lim[x→0] x²/(x²/2)
=2

Answer 2

lim [x→0] x²/(1-cosx)
=lim [x→0] x²/2sin²(x/2)
=4/1lim [x→0] (x/2)²/2sin²(x/2)
=2/1