lim n→0时,求(cosx-1)/x²的极限
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lim n→0时,求(cosx-1)/x²的极限
![lim n→0时,求(cosx-1)/x²的极限](/uploads/image/z/17258111-71-1.jpg?t=lim+n%E2%86%920%E6%97%B6%2C%E6%B1%82%28cosx-1%29%2Fx%26%23178%3B%E7%9A%84%E6%9E%81%E9%99%90)
lim(x-->0) (cosx - 1)/x²
= lim(x-->0) [1 - 2sin²(x/2) - 1]/x²
= lim(x-->0) - 2sin²(x/2)/(x/2)² * 1/4
= lim(x-->0) [sin(x/2)/(x/2)]² * -1/2
= -1/2
= lim(x-->0) [1 - 2sin²(x/2) - 1]/x²
= lim(x-->0) - 2sin²(x/2)/(x/2)² * 1/4
= lim(x-->0) [sin(x/2)/(x/2)]² * -1/2
= -1/2
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