求lim{下面(x属于0)}(1-cosx)/ln(1+x^2)的极限怎么算?
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![求lim{下面(x属于0)}(1-cosx)/ln(1+x^2)的极限怎么算?](/uploads/image/z/1246164-60-4.jpg?t=%E6%B1%82lim%7B%E4%B8%8B%E9%9D%A2%28x%E5%B1%9E%E4%BA%8E0%EF%BC%89%7D%EF%BC%881-cosx%29%2Fln%281%2Bx%5E2%29%E7%9A%84%E6%9E%81%E9%99%90%E6%80%8E%E4%B9%88%E7%AE%97%3F)
求lim{下面(x属于0)}(1-cosx)/ln(1+x^2)的极限怎么算?
求lim{下面(x属于0)}(1-cosx)/ln(1+x^2)的极限怎么算?
求lim{下面(x属于0)}(1-cosx)/ln(1+x^2)的极限怎么算?
lim(x→0)(1-cosx)/ln(1+x^2)
[洛必达法则]
=lim(x→0)sinx/[(2x)/(1+x^2)]
=lim(x→0)[sinx/2x]*(1+x^2)
[sinx和x是等价无穷小量]
=1/2*1
=1/2
1-cosx~1/2x^2
1/2
1/2