学帮网极限与变积分上限问题
来源：学生作业学帮网 编辑：学帮网 时间：2024/05/14 05:11:13
极限与变积分上限问题
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.