Question

求极限lim(x→0)[tan3x/x]

Answer 1

下面的图片解答，运用了三种方法：

1、重要极限 sinx / x = 1 ；

2、等价无穷小代换，这是中国微积分的最爱；

3、罗毕达求导法则。

具体解答如下，若点击放大，图片更加清晰。

Answer 2

lim(x→0)[tan3x/x]=3 lim(3x→0)[tan3x/3x]=3 lim(x→0)[sin3x/3x]lim(x→0)[1/cos3x]=3
lim(x→1)(x^2-2x+1)/(x^2-1)=lim(x→1)(x-1)^2/(x+1)(x-1)=lim(x→1)(x-1)/(x+1)=0

Answer 3

lim(x→0)[tan3x/x]
=lim(x→0)[3x/x]
=3
(1)lim(x---->1)(x-1)/(x+1)
=0/2
=0

Answer 4

lim(x→0)[tan3x/x]
=lim(x→0)3[tan3x/3x]
=3

lim(x→1) (x²-2x+1)/(x²-1)
=lim(x→1) (x-1)²/[(x+1)(x-1)]
=lim(x→1) (x-1)/(x+1)
=0
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