(1/(sinx)^2-1/(x^2))当X趋于0时的极限是多少最好有过程?非常感谢.

Question

(1/(sinx)^2-1/(x^2))当X趋于0时的极限是多少最好有过程?非常感谢.

Answer 1

x->0lim[1/(sinx)^2-1/x^2]=lim[(x^2-(sinx)^2)/(x^2(sinx)^2)]=lim[(x^2-(sinx)^2)/x^4]lim[x^2/(sinx)^2]=lim[(x^2-(sinx)^2)/x^4](之后的使用洛比达法则）=lim[(2x-2sinxcosx)/(4x^3)]=lim[(2-2cos2x)/(12x^2)]=l...