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)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/22 07:39:24
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)
∵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
=2
limx->0[cosx+f(x)+xf'(x)=0
limx->0f(x)=-1
limx->0[cosx+f(x)]/x
=limx->0[-sinx+f'(x)]=f'(x)
∴limx->0[cosx+f(x)+xf'(x)]/x
∴limx->0[cosx+f(x)]/x+limx-->0f'(x)
=2f'(0)
=4
∴f'(0)=2
=limx->0[sinx+xf(x)]/x^2
=limx->0[cosx+f(x)+xf'(x)]/(2x)
=1/2limx->0[cosx+f(x)+xf'(x)]/x
=2
limx->0[cosx+f(x)+xf'(x)=0
limx->0f(x)=-1
limx->0[cosx+f(x)]/x
=limx->0[-sinx+f'(x)]=f'(x)
∴limx->0[cosx+f(x)+xf'(x)]/x
∴limx->0[cosx+f(x)]/x+limx-->0f'(x)
=2f'(0)
=4
∴f'(0)=2
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)
设f(X)连续且满足 f(x)=e^x+sinx- ∫ x 0 (x-t)f(t)dt,并求该函数f(x)
设f(x)为可导函数且满足 limx→0 [f(1)-f(1-x)]/2x = -1 ,则曲线y=f(x)在点(1,f(
设函数f(x)连续,lim((f(x)/x)-1/x-(sinx/x^2))=2,f(0)=?
设f(x)在x=0处连续,且limx->0f(x)-1/x=a(a为常数),求f(0),f'(0)
设函数f(x)满足条件f(x+y)=f(x)+f(y),且f(x)在x=0处连续,证明f(x)在所有的点x0处连续
设F(X)在[0,1连续,且满足f(X)=4X^3-3X^2∫f(x)dx正在考试,求速度
设f(x)在R上满足f(x)的导数=2f(x),且f(0)=1,求函数f(x)
设函数f(x)在x=0处可导且 limx→0{[f(x)+1]/[x+sinx]}=2 则f(x)导数在x=0的值是?
设函数f(x)满足f(x)+2f=x(x不等于0),求f(x)
设当x>0时,函数f(x)连续且满足f(x)=x+∫(1,x)1/xf(t)dt,求f(x)
微积分导数题,急设函数f(x)满足f"(x)+sin^2f'(x)=sinx,且f'(0)=0,则(0,f(0))是拐点