limx趋向于0,x^2/ln(1-3x)=?
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limx趋向于0,x^2/ln(1-3x)=?
limx趋向于0,x^2/ln(1-3x)=?
limx趋向于0,x^2/ln(1-3x)=?
limx^2/ln(1-3x)=lim2x/[-3/(1-3x) ("0/0"型)
x→0 x→0
=(-2/3)limx(x-3x^2)
x→0
=0
利用等价无穷小关系:
ln(1-3x)~-3x
所以
limx→0, x^2/ln(1-3x)
=limx→0, x^2/(-3x)
=-limx→0, x/3
=0
=limx²/﹙﹣3x﹚=0
x^2/ln(1-3x)=0
洛必达法则:x^2/ln(1-3x)=2x/[-3/(1-3x)]=0/-3=0 ( limx趋向于0)
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