设函数f(x)在x=1连续,且f(x)/(x-1)的极限存在,求证f(x)在x=1可导.

设函数f(x)在x=1连续,且f(x)/(x-1)的极限存在,求证f(x)在x=1可导. 一道高数题,设函数f(x)在[0,+∞)上连续,且f(x)=x(e^-x)+(e^x)∫(0,1) f(x)dx,则f(x)=?设函数f(x)在[0,+∞)上连续,且f(x)=x(e^-x)+(e^x) ∫(0,1) f(x)dx ,则f(x)= 设函数f(x)在[0,无穷)上连续可导,且f(0)=1,|f'(x)|0时,f(x) 设函数y=f(x)在[0,1]上连续,且0 设函数y=f(x)在[0,1]上连续,且0 设函数f(x)在[a,b]上连续,在(a,b)内可导且f'(x) 设函数f(x)在[a,b]上连续,在(a,b)上可导且f'(x) 设函数f (x)在x = 0点连续,且f (0) = 0,已知| g (x) | 设函数f(x)具有连续的导数,且函数F(x)(解析式见图)在x=0处连续,求f'(0). 设函数f(x)在x=2处连续,且lim（x→2）f(x)/(x-2)(x→2)=3,求f'(2). 设函数f(x),g(x)在区间[a,b]上连续,且f(a) 设函数f(x)满足条件f(x+y)=f(x)+f(y),且f(x)在x=0处连续,证明f(x)在所有的点x0处连续 设函数f（x）在x=1处连续,且limf（x）/x-1的极限=2,则f(1)等于多少 设f(x)在[0,1]上有二阶连续导数,且满足f(1)=f(0)及|f''(x)| 设函数f(x)在x=0点连续 且满足limx->0(sinx/x^2+f(x)/x)=2求f'(0) .设函数f(x),g(x)在区间[-a,a]上连续,g(x)为偶函数,且f(-x)+f(x)=2.证明： 设f(x)在x=0处连续,且lim(x趋于0）f(x)/x^2=1 ,证明函数f(x)在x=0处可导且取得极小值. 设f(x)在x=0处连续,且lim(x趋于0）f(x)/x^2=1 ,证明函数f(x)在x=0处可导且取得极小值.