一当x>Q时,G(x)=-imx 当x<Q时,G(x)=x 又G"(0)=lim x-0 →G(0)=0 x2+1-1 G'0)=hi2 r-01 于是G(x)在(-①,+0)上可导,且G(x)=f(x) cosx+c x>0 (x=1 x2+1+Cx<0 202//302021/1/30 4 0 cos 1 (0) lim 0 = −  = + → + x x G x 又 0 1 1 2 1 (0) lim 2 0 = + −  = − → − x x G x  G(0) = 0 当x  0时, G(x) = −sin x 于是G(x)在(−, + )上可导,且 G(x) = f (x)      + +  +   =  1 0 2 1 cos 0 ( ) 2 x C x x C x f x dx 当x  0时, G(x) = x