设f(x)是零到正无穷上的连续函数,且f(x)=f(x^2),x属于零到正无穷,证...答:证明:设 x = y^2,f(y)=f(y^2), ===> f(x)= f(x^(1/2))任给x 大于0, 不等于1, f(x) = f(x^(1/2))= f(x^(1/4))=...=f(x^(1/2^n))=...因为 x, x^(1/2), ..., x^(1/2^n), ... ---> 1 根据连续性, 于是 f(1)=lim f(x^(...
设f(x)=x/(1+x^2;)求:答:(1)令y′=(1-x^2)/(1+x^2)^2=0,x=±1,当x<-1时,y′<0;当-1<x<1时,y′>0;当x>1时,y′<0,故f(x)在(-∞,-1)和(1,+∞)上是减函数,在(-1,1)上是增函数.(2)由(1),f(x)在[-2,0]上有x=-1,y′=0,y极小值=f(-1)=-1/2.f(x)在[-2,-1]上是...