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lim(x→0)(1/ln(1+2x)-1/sin2x)
题目详情
lim(x→0)(1/ln(1+2x)-1/sin2x)
▼优质解答
答案和解析
先通分,然后分母用等价无穷小替换,ln(1+2x)~2x,sin2x~2x,
原式=lim[sin2x-ln(1+2x)]/4x^2=lim[2cos2x-2/(1+2x)]/8x=lim[(1+2x)cos2x-1]/4(1+2x)x
=lim[2cos2x-2(1+2x)sin2x]/4
=2/4
=1/2
原式=lim[sin2x-ln(1+2x)]/4x^2=lim[2cos2x-2/(1+2x)]/8x=lim[(1+2x)cos2x-1]/4(1+2x)x
=lim[2cos2x-2(1+2x)sin2x]/4
=2/4
=1/2
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