lim(x→∞)[∫(0积到x）（t²*e^t²）dt]/[x*e^x²]=?

lim(x→∞)[∫(0积到x）（t²*e^t²）dt]/[x*e^x²]=?
lim(x→∞)[∫(0积到x）（t²*e^t²）dt]/[x*e^x²]=?

lim(x→∞)[∫(0积到x）（t²*e^t²）dt]/[x*e^x²]=?
∵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.

这是无穷大比无穷大型
分子分母同取导后再求极限
=lim(x→∞)[(X²）/（2X²+1）]=1/2