求极限lim{(x^2/sinx)×sin1÷x}x趋向0

问题描述:

求极限lim{(x^2/sinx)×sin1÷x}x趋向0

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

lim{(x^2/sinx)×sin1÷x}
=lim x*sin1÷x
-limx∵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