函数f(x)在点x=0处可导,且f(0)=0,f'(0)=1,极限f(2sinx)/x=?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/24 06:25:30
函数f(x)在点x=0处可导,且f(0)=0,f'(0)=1,极限f(2sinx)/x=?
![函数f(x)在点x=0处可导,且f(0)=0,f'(0)=1,极限f(2sinx)/x=?](/uploads/image/z/15078142-46-2.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E7%82%B9x%3D0%E5%A4%84%E5%8F%AF%E5%AF%BC%2C%E4%B8%94f%280%29%3D0%2Cf%27%280%29%3D1%2C%E6%9E%81%E9%99%90f%282sinx%29%2Fx%3D%3F)
利用极限定义.
因f(0)=0,f'(0)=1,故
1=f'(0)=lim [f(t)-f(0)]/(t-0)=lim f(t)/t (令t=2sinx) =lim f(2sinx)/(2sinx)
t->0 t->0 2sinx->0
则lim f(2sinx)/x =lim f(2sinx)/(2sinx)*(2sinx/x)=1*2=2
x->0 2sinx->0
因f(0)=0,f'(0)=1,故
1=f'(0)=lim [f(t)-f(0)]/(t-0)=lim f(t)/t (令t=2sinx) =lim f(2sinx)/(2sinx)
t->0 t->0 2sinx->0
则lim f(2sinx)/x =lim f(2sinx)/(2sinx)*(2sinx/x)=1*2=2
x->0 2sinx->0
函数f(x)在点x=0处可导,且f(0)=0,f'(0)=1,极限f(2sinx)/x=?
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)
设函数f(x)连续,lim((f(x)/x)-1/x-(sinx/x^2))=2,f(0)=?
急切!如果函数f(x)在x=0处可导,且f(0)=0 x趋于0 时:那么求极限f(x) /x=?
设f(x)可导,F(x)=f(x)(1+|sinx|),若F(X)在点x=0处可导,则必有(?)
函数f(x)满足f'(x)=f(x)+1,且f(0)=0,则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
高数导数极限题函数f(x)在点x=0连续lim(x→0)[sinx/x^2+f(x)/x]=2求f’(0)题是不是错了
函数f(x)在x=0点连续,且极限lim(f(x)+3)/x=2,问函数f(x)在x=0点是否可导
分段函数f(x)=sinx (x>=0时);f(x)=x^2(x
设f(x)可导,且f(0)=0,证明F(X)=f(x)(1+/SINX/)在x=0处可导
已知二次函数f(x)满足f(x+1)-f(x)=2x且f(0)=0