证明: 当 $m<2$ 时, $dps{lim_{x o 0^+}cfrac{1}{x^m}int_0^x sin cfrac{1}{t} d t=0}$.
证明: $$eex ea lim_{x o 0^+}cfrac{1}{x^m}int_0^x sin cfrac{1}{t} d t &=lim_{x o 0^+} cfrac{1}{x^m} int_0^x t^2 d cos cfrac{1}{t}\ &=lim_{x o 0^+} cfrac{1}{x^m} sex{x^2coscfrac{1}{x} -int_0^x 2tcoscfrac{1}{t} d t}\ &=-2lim_{x o 0^+} cfrac{int_0^x tcos cfrac{1}{t} d t}{x^m}quadsex{2-m>0}\ &=lim_{x o0^+}cfrac{sex{xi_xcoscfrac{1}{xi_x}}cdot x}{x^m}\ &=0. eea eeex$$