Question

求极限 ①lim x→n- （x-[x]） ②lim x→e log(x-1)/x-e ③limx→0+ log x^x

Answer 1

①lim x→n- （x-[x]）

=n-(n-1)

=1

②lim x→e ln(x-1)/(x-e)

=[lim x→e ln(x-1)*lim x→e [1/(x-e)]

=ln(e-1)*(+∞)

=+∞

③limx→0+ ln x^x

=limx→0+ (lnx)/(1/x)

=limx→0+ (1/x)/(-1/x²)

=limx→0+ (-x)

=0