求一道极限题 X趋于0,1/(X^2) 减 1/ (sin(X))^2如题LIM (X趋于0) 1/(X^2) 减 1/ (sin(X))^2

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求一道极限题X趋于0,1/(X^2)减1/(sin(X))^2如题LIM(X趋于0)1/(X^2)减1/(sin(X))^2求一道极限题X趋于0,1/(X^2)减1/(sin(X))^2如题LIM(X

求一道极限题 X趋于0,1/(X^2) 减 1/ (sin(X))^2如题LIM (X趋于0) 1/(X^2) 减 1/ (sin(X))^2
求一道极限题 X趋于0,1/(X^2) 减 1/ (sin(X))^2
如题
LIM (X趋于0) 1/(X^2) 减 1/ (sin(X))^2

求一道极限题 X趋于0,1/(X^2) 减 1/ (sin(X))^2如题LIM (X趋于0) 1/(X^2) 减 1/ (sin(X))^2
化为(sin(x)^2-x^2)/(x^2*sin(x)^2)
分子分母经过3次罗比他求导,得到：
2*sin(2*x)/(-3*sin(2*x)-6*x*cos(2*x)+2*x^2*sin(2*x))
=2/(-3-6*x/sin(2*x)+2*x^2)
=2/(-3-3)=-1/3
我用matlab算的,是-1/3
>> syms x
>> limit(1/x^2-1/(sin(x))^2,0)
ans =
-1/3

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