可根据导数的定义得
x趋于0,[1-cos(x^2)]/(1-cosx)的极限
=[cos0^2-cos(x^2)]/(cos0-cosx)的极限
=x{[cos0^2-cos(x^2)]/(0^2-x^2)}除以
[(cos0-cosx)/(0-x)] 的极限
=x乘以cos(x^2)的导数/cosx的数 的极限
=x*[-2sin(x^2)}/(-sinx) 的极限
=2sin(x^2)*[x/sinx] 的极限
=2sin(x^2)*[(x-0)/(sinx-sin0)] 的极限
=2sin(x^2)*[1/(sinx的导数)] 的极限
=2sin(x^2)*(1/cosx) 的极限
=2sin(0^2)*(1/cos0)=0