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