lim(x趋向0)ln(1+2x)/(e^sinx-1)
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![lim(x趋向0)ln(1+2x)/(e^sinx-1)](/uploads/image/z/5190820-52-0.jpg?t=lim%28x%E8%B6%8B%E5%90%910%29ln%281%2B2x%29%2F%28e%5Esinx-1%29)
lim(x趋向0)ln(1+2x)/(e^sinx-1)
lim(x趋向0)ln(1+2x)/(e^sinx-1)
lim(x趋向0)ln(1+2x)/(e^sinx-1)
等价无穷小
x->0,ln(1+2x)~2x
e^sinx-1~sinx~x
所以lim x->0,ln(1+2x)/(e^sinx-1)=lim2x/x=2
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