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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)*
题目内容:
(∫(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
(∫(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
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