设h(x)=f(x)-g(x)则h(x)在(a,b)上可导且h'(x)=f'(x)-g'(x)<0∴h(x)在(a,b)上单调递减又f(a)=g(a)∴h(a)=0∴h(x)<0即当x∈(a,b)时，f(x)<g(x)成立 （1）正确∵f(x)和g(x)在[a,b]上有连续导数∴lim(x→x0)f'(x)=f'(x0)lim(x→x0)g'(x)=g'(x0)又f'(x)<g'(x)对任意x∈(a,b)成立∴f'(x0)<g'(x0)即lim(x→x0)f'(x)<lim(x→x0)g'(x)成立 (2)正确x∈(a,b)时，-x∈(-b,-a)无法确定f(x)和g(x)在该区间的性质 (3)不正确设w(x)=∫(0→x)f(t)dt-∫(0→x)g(t)dt则w'(x)=f(x)-g(x)=h(x)由(1)知h(x)<0∴w'(x)<0∴w(x)在(a,b)上单调递减又f(a)=g(a)∴w(a)=0∴w(x)<0即当x∈(a,b)时，∫(0→x)f(t)dt<∫(0→x)g(t)dt成立 （4）正确综上所述，(1),(2),(4)正确
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