来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/07/16 22:05:21
极限与变积分上限问题
![](http://img.wesiedu.com/upload/9/03/903d4e61b2bfe75b229d7b20031ab334.jpg)
做变换 u=x²-t²,则极限
g.e = (1/2)lim(x→0)∫[0,x]f(x²-t²)d(t²)/(x^4)
= (-1/2)lim(x→0)∫[x²,0]f(u)du/(x^4)
= (1/2)lim(x→0)∫[0,x²]f(u)du/(x^4) (0/0)
= (1/2)lim(x→0)[f(x²)(2x)]/(4x^3)
= (1/4)lim(x→0)[f(x²)-f(0)]/(x²)
= (1/4)f'(0)
= 1/4.