1.设曲线y=f(x)过原点,且该曲线在点(x,f(x))处的切线斜率为-2x,则lim[f(-2x)⼀x^2]

2025-03-07 15:27:27
推荐回答(1个)
回答1:

1、条件为f(0)=0,且f'(x)=-2x,于是
lim f(-2x)/x^2=lim -2f'(-2x)/(-2x)=lim 4x/(-2x)=-2.
2、F(x)=f'(x)/e^x,
F'(x)=(f''(x)*e^x-f'(x)*e^x)/(e^x)^2
=(f‘’(x)-f'(x))/e^x>0,
故F(x)=f'(x)/e^x是递增函数。