2題設函數y=sinx+√3︱cosx︱，若y之最大

1.
A
=1-(1/2)+(1/3)-(1/4)+……+(1/1999)-(1/2000)
=1+(1/2)+(1/3)+(1/4)+……+(1/1999)+(1/2000) –2*[(1/2) + (1/4) + (1/6) + …….+(1/2000)]
=1+(1/2)+(1/3)+(1/4)+……+(1/1999)+(1/2000) – [1 + (1/2) +(1/3) +……..+(1/1000)]
=1/1001+1/1002+………+1/2000
=B……………..(解答)

2.
當cos x ＞0時
原式 = 2*sin[x + (π/3)],其最大值 = 2,最小值 = -2
當cos x＜0時
原式 = 2*sin[x - (π/3)] ,其最大值 = 2,最小值 = -2
由此可得(M,m) = (2,-2)…………….(解答)



2010-03-26 18:32:28 補充：
嗯…………忘記cos x有絕對值了!!
當cos x = 0,sin x = -1時,y有最小值 = -1
感謝天助大大的提醒!!

A=B

2010-03-26 13:49:19 補充：
(M,m)=(2, -1)