a> 0, Let f (x) = [(2010x + 1 + 2008) / (2010x + 1)] + SiNx (x belongs to [- A, a]) with the maximum value of M and the minimum value of N, and find m + n =? (where x + 1 in the front bracket is the superscript and X in the back bracket is the superscript)

a> 0, Let f (x) = [(2010x + 1 + 2008) / (2010x + 1)] + SiNx (x belongs to [- A, a]) with the maximum value of M and the minimum value of N, and find m + n =? (where x + 1 in the front bracket is the superscript and X in the back bracket is the superscript)

F (x) = [(2010 ^ (x + 1) + 2008) / (2010 ^ x + 1)] + SiNx let g (x) = (2010 ^ (x + 1) + 2008) / (2010 ^ x + 1), then G (x) = (2010 ^ (x + 1) + 2010-2) / (2010 ^ x + 1) = 2010-2 / (2010 ^ x + 1). Since 2010 ^ x is an increasing function on R, G (x) is also an increasing function on R