求解ln(1+2x)/sin3x(x→0)的极限.为什么ln(1+2x)~2x

Question

求解ln(1+2x)/sin3x (x→0)的极限.
为什么ln(1+2x)~2x

Answer 1

先对分子分母分别求导得
2
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3 cos(3 x) (2 x + 1)
令x=0,则上式等于2/3.