lqf318
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共回答了15个问题采纳率:100% 举报
1 x→0,lim(x².e^(1/x)
=x→0,lim[e^(1/x)/(1/x²)] (适用罗比塔法则)
=x→0,lim[e^(1/x)(-1/x²)/(-1/x³)]
=x→0,lim[e^(1/x)/(1/x)] (再求导)
=x→0,lim[e^(1/x)(-1/x²)/(-1/x²)]
=x→0,lime^(1/x)
=∞
2、 x→1,lim [1/Inx-1/(x-1)]
=x→1,lim [(x-1)-Inx]/[(x-1)Inx] (适用罗比塔法则)
=x→1,lim [1-1/x]/[(x-1)/x+lnx]
=x→1,lim [x-1]/[x-1+xlnx]
=x→1,lim 1/[1+1+lnx]
=x→1,lim 1/[2+lnx]
=1/2
3、x→0,lim [e^(x³)-1-x³]/(sinx)^6
x→0,lim x/sinx为同阶无穷小,替换
=x→0,lim [e^(x³)-1-x³]/(x)^6
=x→0,lim [e^(x³)(3x²)-3x²]/6(x)^5
=x→0,lim [e^(x³)-1]/2x³
=x→0,lim [e^(x³)(3x²)]/6x²
=x→0,lim [e^(x³)]/2
=1/2
1年前
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