lim(x→∞)[∫(0积到x）（t눀乘以e的t눀次方）dt]⼀[x乘以e的x눀次方]=？

解：∵lim(x→∞)[∫(0,x)t²e^(t²)dt]=∞
∴lim(x→∞){[∫(0,x)t²e^(t²)dt]/[xe^(x²)]}=lim(x→∞){[∫(0,x)t²e^(t²)dt]'/[xe^(x²)]'} (∞/∞型极限，应用罗比达法则)
=lim(x→∞){[x²e^(x²)]/[e^(x²)+2x²e^(x²)]}
=lim(x→∞)[x²/(1+2x²)]
=lim(x→∞)[1/(2+1/x²)]
=1/2。

解：原式=lim(x->∞){[∫<0,x>t²e^(t²)dt]'/[xe^(x²)]'} (∞/∞型极限，应用罗比达法则)
=lim(x->∞){[x²e^(x²)]/[e^(x²)+2x²e^(x²)]} (求导数)
=lim(x->∞)[x²/(1+2x²)] (化简)
=lim(x->∞)[1/(1/x²+2)]
=1/(0+2)
=1/2。