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)_数学解答

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)

人气：333 ℃　时间：2020-05-03 08:34:25

解答

∵limx->0(sinx/x^2+f(x)/x)=limx->0[sinx+xf(x)]/x^2=limx->0[cosx+f(x)+xf'(x)]/(2x)=1/2limx->0[cosx+f(x)+xf'(x)]/x=2limx->0[cosx+f(x)+xf'(x)=0limx->0f(x)=-1limx->0[cosx+f(x)]/x=limx->0[-sinx+f'(x)]=f'(x...