极限与变积分上限问题
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 21:03:38
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极限与变积分上限问题
极限与变积分上限问题
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.