赞 lianguobin 花朵
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根据泰勒公式
f(x+h)=f(x)+f'(x)h+(1/2)f''(x)h^2+o(h^2)
于是：f(x)+hf'(x+θh)=f(x)+f'(x)h+(1/2)f''(x)h^2+o(h^2)
θ{[f'(x+θh)-f'(x)]/θh}=(1/2)f''(x)+o(h^2)/h^2
lim(h→0)θ{[f'(x+θh)-f'(x)]/θh}=lim(h→0)[(1/2)f''(x)+o(h^2)/h^2]
lim(h→0)θf''(x)=(1/2)f''(x)
lim(h→0)θ=1/2
f(x+h)=f(x)+f'(x)h+(1/2)f''(x)h^2+o(h^2)
于是：f(x)+hf'(x+θh)=f(x)+f'(x)h+(1/2)f''(x)h^2+o(h^2)
θ{[f'(x+θh)-f'(x)]/θh}=(1/2)f''(x)+o(h^2)/h^2
lim(h→0)θ{[f'(x+θh)-f'(x)]/θh}=lim(h→0)[(1/2)f''(x)+o(h^2)/h^2]
lim(h→0)θf''(x)=(1/2)f''(x)
lim(h→0)θ=1/2
1年前
10
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