第1个回答 2017-11-14
f'(x)=lim(h→0)[f(x+h)-f(x)]/h
∴原极限=lim(h→0){[f(x₀+h)-f(x₀)+f(x₀)]/f(x₀)}^(1/h)
={1+[1/f(x₀)][f(x₀+h)-f(x₀)]·h/h}^(1/h)
={1+[f'(x₀)/f(x₀)]·h}^{[f(x₀)/f'(x₀)]·h·[f'(x₀)/f(x₀)]}
=e^[f'(x₀)/f(x₀)]
∴原极限=lim(h→0){[f(x₀+h)-f(x₀)+f(x₀)]/f(x₀)}^(1/h)
={1+[1/f(x₀)][f(x₀+h)-f(x₀)]·h/h}^(1/h)
={1+[f'(x₀)/f(x₀)]·h}^{[f(x₀)/f'(x₀)]·h·[f'(x₀)/f(x₀)]}
=e^[f'(x₀)/f(x₀)]
第2个回答 2017-11-14
就因为没告诉你，所以只能写成f(x0)和f(x0)’。如果告诉你具体的值，就带进去算出最终结果咯追问
好的吧 谢了
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