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[单选题]
f(x)在区间(-∞,+∞)奇函数,且满足f(1-x)=f(1+x)。若f(1)=2,f(1)+f(2)+f(3)+ +f(50)=()
A.-50
B.0
C.2
D.50
![](https://static.youtibao.com/asksite/comm/h5/images/m_q_a.png)
C、2
![](https://static.youtibao.com/asksite/comm/h5/images/solist_ts.png)
A.-50
B.0
C.2
D.50
C、2
已知函数y=F(x),x∈(-∞,+∞)可导为奇函数,且f(x)≠0,则f"(x)在(-∞,+∞)上一定也是奇函数.( )
参考答案:错误
设f(x)是奇函数,f(1)=a,且f(x+2)-f(x)=f(2). (1)试用a表示,f(2)与f(5); (2)问a取何值时,f(x)以2为周期.
设函数f(x)在无限区间(a,+∞)内有导数f'(x),且
证明:在区间(a,+∞)内至少有一点ξ,使f'(ξ)=0.
设f(x)在区间[a,b]上连续,且f(a)<a,f(b)>b,证明存在ξ∈(a,b),使f(ξ)=ξ.
设f(x)在区间[a,b]上连续,且f(a)<a,f(b)>b,证明存在ξ∈(a,b),使f(ξ)=ξ.
设f(x)在区间[0,1]上可微,且满足条件,试证:存在ξ∈(0,1),使f(ξ)+ξf'(ξ)=0.