设f(x)连续,g(x) =∫(1,0)f(xt)dt,且lim x→0 f(x)/x =A,求 g'(x).
设f(x)连续,g(x) =∫(1,0)f(xt)dt,且lim x→0 f(x)/x =A,求 g'(x).
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如题
其他人气:454 ℃时间:2020-05-24 01:06:06
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x>0时,g(x)=∫(0,1)f(xt)(1/x)dxt=1/x∫(0,x)f(y)dy.所以g'(x)=(-1/x^2)∫(0,x)f(y)dy + f(x)/x.x=0时,lim x→0 f(x)/x =A,所以lim x→0 f(x)=0,所以f(0)=0,所以g(0)=0.所以g'(0)=lim x→0 g(x)/x=lim x→0 ∫(0,1)f...
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