例21、设f()连续,9(x)=0fxdt,且m)=A 求φ(x),并讨论q(x)在ⅹ=0处连续性 解:m)=A:f0)=lnf(x)=0得o()=0 令Mt=uq(x) f(udux≠0 ∫。f(u)dux≠0 0(x=mn9(x)-(0) fudu =lim +2=lim i(x)a xf(x) (udu 0 =0 X) fudu f udu lim p (x)=lim AA 22 ∴φ'(x)在ⅹ=0连续 即qp'(x)在(∞,+∞)连续14 例 21、设 f(x) 连续，  =  1 0 (x) f(xt)d t ，且 A x f(x) lim x 0 = → 求  (x) ，并讨论  (x) 在 x = 0 处连续性 解： A f(0) lin f(x) 0 x f(x) lim x 0 x 0 =  = = → →  得 (0) = 0 令 xt = u  =  x 0 f(u)d u x 1 (x) x  0      =   =  0 x 0 f(u)d u x 0 x 1 (x) x 0 2 A 2x f(x) lim x f(u)du lim x - 0 (x) - (0) (x) lim x 0 2 x 0 x 0 x 0 = = =   =   → → →  ∴        =  − =    x 0 2 A x 0 x xf(x) f(u)du (x) 2 x 0 (0) 2 A 2 A A - ) x f(u)du x f(x) lim( x xf(x) f(u)du lim (x) lim / 2 x 0 x 0 2 x 0 x 0 / x 0   = = = = − − =   → → → ∴  (x) 在 x = 0 连续 即  (x) 在 (− ,+) 连续