对于函数f(x),f(x)

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对于函数f(x),f(x)对于函数f(x),f(x)对于函数f(x),f(x),f(x)=(x+1)^2/(x^2+1)=(x^2+2x+1)/(x^2+1)=1+2x/(x^2+1)≤1+(x^2+

对于函数f(x),f(x)
对于函数f(x),f(x)

对于函数f(x),f(x)
,f(x)=(x+1)^2/(x^2+1)
=(x^2+2x+1)/(x^2+1)
=1+2x/(x^2+1)
≤1+(x^2+1)/(x^2+1) x^2+1≥2√(x^2*1)=2x
=2
所以,f(x)=(x+1)^2/x^2+1 的上确界是2

(x+1)^2/(x^2+1)
=x^2+2x+1/(x^2+1)
=1+2x/(x^2+1)
2x<=(x^2+1)
2x/(x^2+1)<=1
所以(x+1)^2/(x^2+1)<=2 (当x=1时)