设函数f(x)在(a,+∞ )上可导,且lim(x->+∞ )(f(x)+f'(x))=0,证明:lim(x->+∞ )f(x)=0
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 18:04:36
![设函数f(x)在(a,+∞ )上可导,且lim(x->+∞ )(f(x)+f'(x))=0,证明:lim(x->+∞ )f(x)=0](/uploads/image/z/3857519-47-9.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%28a%2C%2B%E2%88%9E+%29%E4%B8%8A%E5%8F%AF%E5%AF%BC%2C%E4%B8%94lim%28x-%3E%2B%E2%88%9E+%29%28f%28x%29%2Bf%27%28x%29%29%3D0%2C%E8%AF%81%E6%98%8E%3Alim%28x-%3E%2B%E2%88%9E+%29f%28x%29%3D0)
设函数f(x)在(a,+∞ )上可导,且lim(x->+∞ )(f(x)+f'(x))=0,证明:lim(x->+∞ )f(x)=0
设函数f(x)在(a,+∞ )上可导,且lim(x->+∞ )(f(x)+f'(x))=0,证明:lim(x->+∞ )f(x)=0
设函数f(x)在(a,+∞ )上可导,且lim(x->+∞ )(f(x)+f'(x))=0,证明:lim(x->+∞ )f(x)=0
证明:∵lim(f(x)+f'(x))=0
∴对任意正数ε>0,存在一个与之有关的正数M(x),使得当x>M时
-ε
设函数f(x)在[a,b]上连续,在(a,b)上可导且f'(x)
设函数f(x)在(a,+∞ )上可导,且lim(x->+∞ )(f(x)+f'(x))=0,证明:lim(x->+∞ )f(x)=0
设函数f x,gx在[a,b]上可导,且f'x
设函数f(x),g(x)在[a,b]上可导,且f'(x)>g'(x),则当a
设函数f(x)在[a,b]上连续,在(a,b)内可导且f'(x)
设函数f(x)在[0,1]上可导,且0
设函数f(x)在[0,1]上可导,且0
设函数f(x)在区间(-∞,+∞)上是减函数、且f(1-a)
设函数f(x)在区间(-∞,+∞)上是减函数、且f(1-a)
设函数f(x),g(x)在[a,b] 上均可导,且f'(x)
设函数f(x),g(x)在区间[a,b]上连续,且f(a)
设函数f(x)在(-∞,+∞)上可导,若实数a,使f'(x)+af(x)
设函数f(x)在[a,b]可导 且f'(x)
设函数f(x)在R上是偶函数,在区间(-∞,0)上递增,且f(a+1)
设函数fx在(0,+∞)上可导,且f(e^x)=x+e^x,则f`(1)=__
设函数f(x)在(-∞,+∞)上可导,且a,b是f(x)=0的两个实根.证明:方程f(x)+f'(x)=0在(a,b)内至少有一个实根.
设函数f(x)在R上可导,且对任意x∈R有|f‘(x)|
设f(x)在[a,b]上二阶可导,且f''(x)>0,证明:函数F(x)=(f(x)-f(a))/(x-a)在(a,b]上单调增加