(∫(0到x)t*e^t*sint dt)/x^6*e^x,求极限,x趋于0
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(∫(0到x)t*e^t*sint dt)/x^6*e^x,求极限,x趋于0
这样做对吗?
=2x*x^2*e^(x^2)*sinx^2/6x^5*e^x+x^6*e^x
=2x^5*e^(x^2)/e^x(6x^5+x^6)
=2x^5{(e^(x^2)-1) +1}/{(e^x-1)+1}(6x^5+x^6)
=2x^5(x^2+1)/(x+1)(6x^5+x^6)
=2x^7+2x^5/7x^6+x^7+6x^5
由于x趋于0,x^7 和x^6是 x^5的高阶无穷小,所以
=2x^5/6x^5=1/3
(∫(0到x^2)t*e^t*sint dt)/x^6*e^x,求极限,x趋于0,刚才的错了
这样做对吗?
=2x*x^2*e^(x^2)*sinx^2/6x^5*e^x+x^6*e^x
=2x^5*e^(x^2)/e^x(6x^5+x^6)
=2x^5{(e^(x^2)-1) +1}/{(e^x-1)+1}(6x^5+x^6)
=2x^5(x^2+1)/(x+1)(6x^5+x^6)
=2x^7+2x^5/7x^6+x^7+6x^5
由于x趋于0,x^7 和x^6是 x^5的高阶无穷小,所以
=2x^5/6x^5=1/3
(∫(0到x^2)t*e^t*sint dt)/x^6*e^x,求极限,x趋于0,刚才的错了
![(∫(0到x)t*e^t*sint dt)/x^6*e^x,求极限,x趋于0](/uploads/image/z/15122388-12-8.jpg?t=%EF%BC%88%E2%88%AB%EF%BC%880%E5%88%B0x%EF%BC%89t%2Ae%5Et%2Asint+dt%EF%BC%89%2Fx%5E6%2Ae%5Ex%2C%E6%B1%82%E6%9E%81%E9%99%90%2Cx%E8%B6%8B%E4%BA%8E0)
积分区间是(0,x^2)吧
上面步骤都是对的,下面可以简化一点
=lim(x->0)2x^5*e^(x^2)/e^x(6x^5+x^6) x->0时e^x^2/e^x=e^(x^2-x)->1
=lim(x->0)2x^5/(6x^5+x^6)
=1/3
上面步骤都是对的,下面可以简化一点
=lim(x->0)2x^5*e^(x^2)/e^x(6x^5+x^6) x->0时e^x^2/e^x=e^(x^2-x)->1
=lim(x->0)2x^5/(6x^5+x^6)
=1/3
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