求极限(给出过程)lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x

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求极限(给出过程)lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x

求极限(给出过程)lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x
求极限(给出过程)
lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x

求极限(给出过程)lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x
x→∞时,sin(2/x)等价于2/x,所以
lim(x→∞) 【(3x^2+5)/(5x+3)】×sin(2/x)
=lim(x→∞) 【(3x^2+5)/(5x+3)】×2/x
=lim(x→∞) (3+5/x^2)/(5+3/x^2)
=(3+0)/(5+0)
=3/5

lim(x趋于∞) 【(3x^2+5)/(5x+3)】×sin2/x =lim(x趋于∞)[(3+5/x^2)/(5+3/x)]×xsin2/x =lim(x趋于∞) (3/5)×2[(sin2/x)/(2/x)] =(3/5)×2×1 =6/5