Question

当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.

Answer 1

lim(1/sin^2x-1/x^2)

=lim(x^2-sin^2x)/(x^2sin^2x)

=lim(x^2-sin^2x)/(x^4)

=lim(2x-sin2x)/4x^3

=lim(2-2cos2x)/12x^2

=lim4sin2x/24x

=1/3