Question

【1】求函数f(x)=cosx+sinx,x∈[0,π]的值域.

Answer 1

1、

f(x)=cosx+sinx=√2sin(x+π/4)

∵x∈[0,π]

∴x+π/4∈[π/4,5π/4]

∴值域为[-1,√2]

2、

b(n+1)-bn=a(n+1)+a(n+2)-an-a(n+1)

=a(n+2)-an

∵｛an}是等差数列,设公差为d

则a(n+2)-an=2d

所以数列｛bn}是等差数列