Question

若lim_x->0 f(x)/x^2=2,则lim_x->0 f(x)/1-cosx=

Answer 1

lim_x->0 f(x)/(1-cosx)

=lim_x->0 [f(x)/x^2]*[x^2/(1-cosx)]

=lim_x->0 [f(x)/x^2]* lim_x->0 [x^2/(1-cosx)]

=2*lim_x->0 [x^2/(1-cosx)]

=2*2

=4

(因为1-cosx = x^2/2+o(x^2),所以 lim_x->0 [x^2/(1-cosx)] ＝ lim_x->0 x^2/(x^2/2) = 2.)