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已知函数f(x)=x2-4,设曲线y=f(x)在点(xn,f(xn))处的切线与x轴的交点...
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已知函数f(x)=x
2-4,设曲线y=f(x)在点(x
n,f(x
n))处的切线与x轴的交点为(x
n+1,0)(n∈N*),其中x
1为正实数.
(Ⅰ)用x
n表示x
n+1;
(Ⅱ)若x
1=4,记
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEoAAAAxCAYAAAB9NT9zAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
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/RQ54p3As1HU92OHCb4W1KcrigFBQcTCqKailvu9Du14oISALBt9DTp648OWOIrlYhsPlIr+kFsB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)
,证明数列{a
n}成等比数列,并求数列{x
n}的通项公式;
(Ⅲ)若x
1=4,b
n=x
n-2,T
n是数列{b
n}的前n项和,证明T
n<3.
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已知函数f(x)=x2-4,设曲线y=f(x)在点(xn,f(xn))处的切线与X轴的交点为(xn+1,0)(n∈N*,xn为正数).
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已知函数f(x)=x2-4,设曲线y=f(x)在点(xn,f(xn))处的切线与x轴的交点为(xn+1,0)(n∈N*),其中x1为正实数.
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