求极限lim{(x^2/sinx)×sin1÷x}x趋向0
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求极限lim{(x^2/sinx)×sin1÷x}x趋向0
求极限lim{(x^2/sinx)×sin1÷x}x趋向0
求极限lim{(x^2/sinx)×sin1÷x}x趋向0
lim{(x^2/sinx)×sin1÷x}
=lim x*sin1÷x
-limx<=lim x*sin1÷x<=limx
∵0<=lim x*sin1÷x<=0
∴lim{(x^2/sinx)×sin1÷x}=0
lim{(x^2/sinx)×sin1÷x}x趋向0
=lim(x--->0)(x^2 /sinx)*lim(x--->0)(sin(1/x)
=0*有界量
=0
对
此极限值为0.(x^2/sinx)sin(1/x)=xsin(1/x).在x→0时,sin(1/x)值在-1到+1之间,有限值乘0极限0