因为|xsinx/(x^2+1)|=|x||sinx|/(x^2+1)，且-1<=|sinx|<=1
所以-|x|/(x^2+1)<=|xsinx/(x^2+1)|<=|x|/(x^2+1)
又因为-|xsinx/(x^2+1)|<=xsinx/(x^2+1)<=|xsinx/(x^2+1)|
所以-|x|/(x^2+1)<=xsinx/(x^2+1)<=|x|/(x^2+1)
因为lim(x->∞)±|x|/(x^2+1)=0
所以根据极限的夹逼性，lim(x->∞)xsinx/(x^2+1)=0
0=lim-x/(x²+1)≤lim≤limx/(x²+1)=0
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