lim(x→∞)[∫(0积到x)(t²乘以e的t²次方)dt]/[x乘以e的x²次方]=?
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![lim(x→∞)[∫(0积到x)(t²乘以e的t²次方)dt]/[x乘以e的x²次方]=?](/uploads/image/z/5295289-49-9.jpg?t=lim%28x%E2%86%92%E2%88%9E%29%5B%E2%88%AB%280%E7%A7%AF%E5%88%B0x%EF%BC%89%EF%BC%88t%26%23178%3B%E4%B9%98%E4%BB%A5e%E7%9A%84t%26%23178%3B%E6%AC%A1%E6%96%B9%EF%BC%89dt%5D%2F%5Bx%E4%B9%98%E4%BB%A5e%E7%9A%84x%26%23178%3B%E6%AC%A1%E6%96%B9%5D%3D%3F)
lim(x→∞)[∫(0积到x)(t²乘以e的t²次方)dt]/[x乘以e的x²次方]=?
lim(x→∞)[∫(0积到x)(t²乘以e的t²次方)dt]/[x乘以e的x²次方]=?
lim(x→∞)[∫(0积到x)(t²乘以e的t²次方)dt]/[x乘以e的x²次方]=?
∵lim(x→∞) ∫(0→x) [t²e^(t²)]dt→∞
lim(x→∞) [xe^(x²)]→∞
∴原式为∞/∞型未定式,用L'Hospital法则,分子分母同时对x求导
原式=lim(x→∞) { ∫(0→x) [t²e^(t²)]dt}'/[xe^(x²)]'
=lim(x→∞) [x²e^(x²)]/[e^(x²)+2x²e^(x²)]
=lim(x→∞) x²/(1+2x²)
=lim(x→∞) 1/[(1/x²)+2]
=1/2