lim{x->0} (1/x) ∫[0, 1] f(xt) dt
= ∫[0, 1] t*lim{xt->0}{f(xt)-f(0)}/(xt) dt
= ∫[0, 1] t*f'(0) dt,注意：lim{xt->0}{f(xt)-f(0)}/(xt) = f'(0)
= f'(0)(0.5t^2) from 0 to 1
= 0.5f'(0)
美国高中数学老师
求x趋于0时lim(1/x)积分符号(上1下0)f(xt)dt
求x趋于0时lim(1/x)积分符号(上1下0)f(xt)dt
f(x)可导,连续,f(0)=0 （答案是0.5f'(0),
f(x)可导,连续,f(0)=0 （答案是0.5f'(0),
数学人气：542 ℃时间：2020-06-12 17:36:13
优质解答
我来回答
类似推荐
- 设f(x)连续,g(x) =∫(1,0)f(xt)dt,且lim x→0 f(x)/x =A,求 g'(x).
- 设连续函数f﹙x﹚满足lim﹙x→0﹚f﹙x﹚/x=2 ,令F﹙x﹚=∫﹙0,1﹚f﹙xt﹚dt ,则F′﹙0﹚= _______
- f(x)二阶可导,g(x) =∫(0,1)f(xt)dt,且lim x→0 f(x)/x =A问g'(x)在x=0处是否连续
- 证明：若函数f(x)∈C[0,+∞],且lim(x->+∞)f(x)=A,则lim(x->+∞)[1/x*∫(0->x)f(t)dt]=A
- 设F(x)=∫(0趋向x) [(x-t)f(t)dt]/(sinx)^2 求lim(x趋向0)F(x),f(0)存在,