lim(x趋近于+∞)(∫e^t²dt)²/∫e^2t²dt 等于多少?
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![lim(x趋近于+∞)(∫e^t²dt)²/∫e^2t²dt 等于多少?](/uploads/image/z/8865540-36-0.jpg?t=lim%EF%BC%88x%E8%B6%8B%E8%BF%91%E4%BA%8E%2B%E2%88%9E%EF%BC%89%EF%BC%88%E2%88%ABe%5Et%26%23178%3Bdt%29%26%23178%3B%2F%E2%88%ABe%5E2t%26%23178%3Bdt+%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
lim(x趋近于+∞)(∫e^t²dt)²/∫e^2t²dt 等于多少?
lim(x趋近于+∞)(∫<0到x>e^t²dt)²/∫<0到x>e^2t²dt 等于多少?
lim(x趋近于+∞)(∫e^t²dt)²/∫e^2t²dt 等于多少?
∞/∞型,洛必达法则
原式=lim(x趋近于+∞)2e^(x²)∫<0到x>e^t²dt / e^(2x²)
=lim(x趋近于+∞)2∫<0到x>e^t²dt / e^(x²)
用次洛必达
=lim(x趋近于+∞)2e^x² / 2xe^(x²)
=lim(x趋近于+∞)1/x
=0