已知limx趋近0 [6+f(x)]/x^2=36,求limx趋近0 [(sin6x)+xf(x)]/x^3=?求详细解答
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已知limx趋近0 [6+f(x)]/x^2=36,求limx趋近0 [(sin6x)+xf(x)]/x^3=?
求详细解答
等于0
lim(x→0) [6+f(x)]/x^2=36
由于分母是无穷小,因此
lim(x→0) [6+f(x)]=0
因此lim(x→0) f(x)=-6
且f(x)与x^2是等阶无穷小
lim(x→0) [6+f(x)]/x^2 (0/0)
=lim(x→0) f'(x)/(2x)
=lim(x→0) f''(x)/2
=36
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lim(x→0) [6+f(x)]/x^2=36
由于分母是无穷小,因此
lim(x→0) [6+f(x)]=0
因此lim(x→0) f(x)=-6
且f(x)与x^2是等阶无穷小
lim(x→0) [6+f(x)]/x^2 (0/0)
=lim(x→0) f'(x)/(2x)
=lim(x→0) f''(x)/2
=36
=lim(x→0) f''(x)=18
lim(x→0) [(sin6x)+xf(x)]/x^3
=lim(x→0) (sin6x-6x)/x^3+lim(x→0) x[f(x)+6]/x^3
=lim(x→0) 6(cos6x-1)/(3x^2)+lim(x→0) [f(x)+6]/x^2
=lim(x→0) 2(cos6x-1)/(x^2)+lim(x→0) f'(x)/(2x)
=lim(x→0) 2*1/2*(6x)^2/(x^2)+lim(x→0) f'(x)/(2x)
=lim(x→0)(6x)^2/(x^2)+lim(x→0) f''(x)/2
=36+9
=45
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已知{limx趋近0 [(sin6x)+xf(x)]/x^3}=0 求limx趋近0 [6+f(x)]/x^2=?答案是36.
已知limx趋近0 [6+f(x)]/x^2=36,求limx趋近0 [(sin6x)+xf(x)]/x^3=?求详细解答
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