lim (x趋近于无穷大)[∫(0,x)t^2*e^(t^2-x^2)dt]/x

问题描述:

lim (x趋近于无穷大)[∫(0,x)t^2*e^(t^2-x^2)dt]/x

lim (x趋近于无穷大)[∫(0,x)t^2*e^(t^2-x^2)dt]/x
=lim (x趋近于无穷大)[∫(0,x)t^2*e^(t^2)dt]/(x*e^(x^2)) 罗比达法则
lim (x趋近于无穷大)[x^2*e^(x^2)]/[e^(x^2)+2x^2*e^(x^2)]
=lim (x趋近于无穷大)x^2/(1+2x^2)
=1/2