Question

limx趋向于0(1/sin^(2)x-1/x^2) 洛必达法则

Answer 1

lim(x->0)(1/(sinx)^2-1/x^2)

=lim(x->0)[x^2-(sinx)^2]/x^4

=lim(x->0)(x+sinx)/x*lim(x->0)(x-sinx)/x^3

=2lim(x->0)(1-cosx)/(3x^2)

=2/3*lim(x->0)1/2x^2/x^2

=1/3