设f (x)在x=0处可导,且f (0)=0,求证：lim(x→∞)f (tx)-f (x)/x=(t-1)f' (0)

函数f（x）在点x=0处可导,且f(0)=0求: (1).lim(x→0)f(x)/x (2)lim(x→0)[f(tx 求证连续函数f(x)满足:∫(0到1)f(tx)dt=f(x)+xsinx 设f(x)是可导函数且f(0)=0,F(x)=∫t^(n-1)f(x^n-t^n)dt,求lim(x→+∞)F(x)/x 设f(x)具有连续导数,且满足f(x)=x+∫(上x下0)tf'(x-t)dt求lim(x->-∞)f(x) 设f(x)有二阶导数,且f''(X)>0,lim(x趋于0）f(x)/x=1 ..证明：当x>0时,有f(x)>x 设y=f(x)在点x0处可导,且f(x0)为最大值,求lim△x→0 f(xo+△x)-f(x0)/△x 设f(x)在x=0处连续,且lim(x趋于0)f(x)/x存在,证明,f(x)在x=0处可导 f(x)在x=a处有二阶导数,求证x趋于0时lim(((f(a+x)-f(a)/x}-f‘(a))/x=1/2f''(a 设函数f(x)在(a,+∞ )上可导,且lim(x->+∞ )(f(x)+f'(x))=0,证明:lim(x->+∞ ) 设f（x）在x=0处连续,且lim （f（x）-1）/x=-1,x→0.,求f(0) 设f(x)在x=0的某一邻域内二阶可导,且lim(x-->0)f(x)/x=0,f''(0)=2.求lim(x-->0) 设函数f(x)在x=1处可导,且f'(1)=2,则[lim(h→0)f(1-h)-f(1)]/h等于