求极限limxsin2x/x^2+1,x为趋向无穷

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求极限limxsin2x/x^2+1,x为趋向无穷求极限limxsin2x/x^2+1,x为趋向无穷求极限limxsin2x/x^2+1,x为趋向无穷答:lim(x→∞)xsin2x/(x^2+1)=

求极限limxsin2x/x^2+1,x为趋向无穷
求极限limxsin2x/x^2+1,x为趋向无穷

求极限limxsin2x/x^2+1,x为趋向无穷
答:
lim(x→∞) xsin2x/(x^2+1)
=lim(x→∞) sin2x/(x+1/x)
=lim(x→∞) sin2x/x
=0
(因为:sin2x总是有界,属于[-1,1],而x是无穷)

limxsin2x/(x^2+1) ?
-lim|x/(x^2+1)| <=limxsin2x/(x^2+1) <=lim|x/(x^2+1) |
则0 <=limxsin2x/(x^2+1) <=0
∴ limxsin2x/(x^2+1)=0