Question

高数极限问题limf(x)/x=1(x趋近于0）求lim（根号下1+f（x）减去1）/x（x趋近于0）我这样做为什么不可

Answer 1

lim(x->0) f(x) /x ( 0/0 ,=> f(0) =0 )

=lim(x->0) f'(x)

=f'(0) =1

lim(x->0) [√(1+f(x) ) - 1]/x (0/0)

lim(x->0) f'(x) /[2√(1+f(x) )]

=f'(0)/[2√(1+f(0) )]

=1/2