求lim(x→∞)1-cos2x/xsinx

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求lim(x→∞)1-cos2x/xsinx

求lim(x→∞)1-cos2x/xsinx
求lim(x→∞)1-cos2x/xsinx

求lim(x→∞)1-cos2x/xsinx
1-cos2x=1-(1-2*(sinX)^2)=2*(sinX)^2,1-cos2x/xsinx=2sinx/x
因为当x→∞时,1/x→0
又sinx为有界函数,|sinx|≤1
所以lim【x→∞】sinx/x=0
lim(x→∞)1-cos2x/xsinx=0