当x趋于0时,x^3-sin(x^2)与sin(x^2)是等价无穷小吗?
求当x趋于0时 极限lim x^3-sin(x^2) / x^2=
老师说 x^3-sin(x^2)与x^2为等价无穷小
可是我算 lim x^3-sin(x^2)/ sin(x^2)= x^3/x^2 - 1=x-1 =-1
-1 也是等价无穷小吗?
我写的极限应该等于1还是-1?
人气:427 ℃ 时间:2020-06-22 23:02:09
解答
你们老师的说法错了只能说是同阶,不能说等价.等价无穷小只能在乘除的情况下能用,你的算法是错的,用洛必达法则不能把他们分开.答案是-1正确的算法是
lim x^3-sin(x^2)/ sin(x^2)
= x^3-sin(x^2)/x^2 (等价无穷小)
=3x^2-2xcos(x^2)/2x (洛必达法则)
=3x/2-cos(x^2)
=-1
记得,算等价无穷小时不能分开,很容易出错的.
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