lim(x-0)sinx-x/x^3的极限
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lim(x-0)sinx-x/x^3的极限
![](http://img.wesiedu.com/upload/9/40/9406089157c3fe903f485a9796e6ecdd.jpg)
![](http://img.wesiedu.com/upload/9/40/9406089157c3fe903f485a9796e6ecdd.jpg)
![lim(x-0)sinx-x/x^3的极限](/uploads/image/z/5755315-67-5.jpg?t=lim%28x-0%29sinx-x%2Fx%5E3%E7%9A%84%E6%9E%81%E9%99%90)
可以用洛必达法则.
原式=lim(x→0)(cosx-1)/(3x^2)
=lim(x→0)-2sin^2(x/2)/(3x^2)
=lim(x→0)-2(x/2)^2/(3x^2)
=-1/6
也可以把sinx泰勒展开.
原式=lim(x→0)(x-x^3/6+o(x^3)-x)/x^3
=lim(x→0)(-x^3/6+o(x^3))/x^3
=lim(x→0)-1/6+o(1)
=-1/6
原式=lim(x→0)(cosx-1)/(3x^2)
=lim(x→0)-2sin^2(x/2)/(3x^2)
=lim(x→0)-2(x/2)^2/(3x^2)
=-1/6
也可以把sinx泰勒展开.
原式=lim(x→0)(x-x^3/6+o(x^3)-x)/x^3
=lim(x→0)(-x^3/6+o(x^3))/x^3
=lim(x→0)-1/6+o(1)
=-1/6