设曲线y=f(x)和y=x^2-x在点(1,0)处有公共的切线,则lim(n趋向于无穷大)nf(n⼀n+2)

2025-06-20 19:40:27
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回答1:

y=x^2-x,
y'=2x-1,y'(1)=1,
曲线y=f(x)和y=x^2-x在点(1,0)处有公共的切线,则
f(1)=0,f'(1)=1,
n→∞时nf[n/(n+2)]=f[n/(n+2)]/(1/n)=f'[n/(n+2)]*2/(n+2)^2/(-1/n^2)
→-2f'(1)=-2.