作业帮limx趋近于-0∫0√x sin(x^2)dx/√(x^3)
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limx趋近于-0∫0√x sin(x^2)dx/√(x^3)
limx趋近于-0∫0√x sin(x^2)dx/√(x^3)
limx趋近于-0∫0√x sin(x^2)dx/√(x^3)
原式=lim(x->0-)[(sinx/(2√x))/(3√x/2)] (0/0型极限,应用罗比达法则)
=lim(x->0-)[(1/3)(sinx/x)]
=(1/3)lim(x->0-)(sinx/x)
=(1/3)*1 (应用重要极限lim(z->0)(sinz/z)=1)
=1/3
limx趋近于-0∫0√x sin(x^2)dx/√(x^3)
limx趋近于-0∫0√x sin(x^2)dx/√(x^3)
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