lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(x)]/x {定积分上限是x,下限为0}我知道用到洛必达法则,5,不是d(x)~原题应为lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(t)]/x {定积分上限是x,下限为0}
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![lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(x)]/x {定积分上限是x,下限为0}我知道用到洛必达法则,5,不是d(x)~原题应为lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(t)]/x {定积分上限是x,下限为0}](/uploads/image/z/2003053-13-3.jpg?t=lim%28x%E8%B6%8B%E8%BF%91%E6%97%A0%E7%A9%B7%29%5B%E2%88%ABt%5E2+e%5E%28t%5E2-x%5E2%29d%28x%29%5D%2Fx+%7B%E5%AE%9A%E7%A7%AF%E5%88%86%E4%B8%8A%E9%99%90%E6%98%AFx%2C%E4%B8%8B%E9%99%90%E4%B8%BA0%7D%E6%88%91%E7%9F%A5%E9%81%93%E7%94%A8%E5%88%B0%E6%B4%9B%E5%BF%85%E8%BE%BE%E6%B3%95%E5%88%99%2C5%2C%E4%B8%8D%E6%98%AFd%28x%29%7E%E5%8E%9F%E9%A2%98%E5%BA%94%E4%B8%BAlim%28x%E8%B6%8B%E8%BF%91%E6%97%A0%E7%A9%B7%29%5B%E2%88%ABt%5E2+e%5E%28t%5E2-x%5E2%29d%28t%29%5D%2Fx+%7B%E5%AE%9A%E7%A7%AF%E5%88%86%E4%B8%8A%E9%99%90%E6%98%AFx%EF%BC%8C%E4%B8%8B%E9%99%90%E4%B8%BA0%7D)
lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(x)]/x {定积分上限是x,下限为0}我知道用到洛必达法则,5,不是d(x)~原题应为lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(t)]/x {定积分上限是x,下限为0}
lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(x)]/x {定积分上限是x,下限为0}
我知道用到洛必达法则,5,
不是d(x)~原题应为lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(t)]/x {定积分上限是x,下限为0}
lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(x)]/x {定积分上限是x,下限为0}我知道用到洛必达法则,5,不是d(x)~原题应为lim(x趋近无穷)[∫t^2 e^(t^2-x^2)d(t)]/x {定积分上限是x,下限为0}
用洛必达法则时,需要先把e^(-x^2)提取出来,放到分母上去,然后再分子分母求导(还应该先说明分子的极限为什么是∞,才能用洛必达法则.)
由此原式=lim(x→∞) [x^2×e^(x^2)]/[e^(x^2)+2x^2×e^(x^2)]=lim(x→∞) x^2/[1+2x^2)]=lim(x→∞) 1/[2+1/x^2)]=1/2
请看原题,d(x)应该是dt吧?
另外,x趋近无穷是正无穷还是负无穷?是d(t),不好意思~~x趋近无穷....以下按照x趋近正无穷理 lim[∫t^2 e^(t^2-x^2)dt]/x =lim[∫t^2 e^(t^2)dt]/xe^(x^2) (这一步把分子中的e^(-x^2) 提到积分号外,并放到分母中; 此时用洛必达法则,答案是0.5)...
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请看原题,d(x)应该是dt吧?
另外,x趋近无穷是正无穷还是负无穷?
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