(arcsinx-x)/[x^2*ln(1+2x)] 在x趋于0时的极限
人气:132 ℃ 时间:2019-11-09 13:43:22
解答
用等价无穷小替换和洛必达法则,原式=lim(x→0)(arcsinx-x)/(2x^3)=lim(x→0)(1/√(1-x^2)-1)/(6x^2)=lim(x→0)(1-√(1-x^2))/(6x^2)*1/√(1-x^2)=lim(x→0)x^2/(1+√(1-x^2))*1/(6x^2)*1/√(1-x^2)=lim(x→0)1/6*1/(...
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