x→∞ lim(3x+sinx)/(2x-sinx)=
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x→∞lim(3x+sinx)/(2x-sinx)=x→∞lim(3x+sinx)/(2x-sinx)=x→∞lim(3x+sinx)/(2x-sinx)=原式=lim(x->∞)(3+sinx/x)
x→∞ lim(3x+sinx)/(2x-sinx)=
x→∞ lim(3x+sinx)/(2x-sinx)=
x→∞ lim(3x+sinx)/(2x-sinx)=
原式=lim(x->∞) (3+sinx/x)/(2-sinx/x)
因为sinx是有界量,1/x为无穷小量
所以当x->∞时,sinx/x->0
所以原式=3/2
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