推 yizihappyQ : 謝謝！ 12/02 19:10
※ 引述《yizihappyQ (Ms.Q)》之銘言：
: https://i.imgur.com/ZFT3oR6.jpg
: 請問這題要怎麼做？
: 要畫圖還是代數？
: 我是用平方想的
: 但是感覺不是很清楚@@
平方不錯, 不過要注意正負號
f^2 (x) = 1 + sinx + 1 - sinx + 2√(1+sinx)(1-sinx)
= 2 + 2√(1-sin^2 x)
= 2 + 2√(cos^2 x)
= 2 + 2 |cosx| ←注意這裡
加絕對值的原因是開根號恆正, 由此知 C 不選 (週期為π), D 選 (cos 為偶函數)
然後兩邊開根號
先看 cosx≧0 即 -π/2≦x≦π/2 的部份
f^2 (x) = 4 [(1 + cosx) / 2]
f(x) = 2√[(1+cosx)/2] = 2cos(x/2)
由此 A 為 f(2π/5) = 2cos(π/5), 可選
B 則由週期知 f(4π/5) = f(-π/5) = 2cos(-π/10), 故不選
這裡不能直接套上式, 因為差了正負號的關係 -- 不過真要套半角也行:
對 π/2≦x≦3π/2, f(x) = 2√[(1-cosx)/2] = 2sin(x/2)
故 f(4π/5) = 2sin(2π/5)
E 則直接看一個週期範圍即可, -π/2≦x≦π/2 範圍內 cos(x/2) 的極小值在兩邊
即 x = ±π/2 時, 此時函數值為 2cos(π/4) = 2*(√2/2) = √2, 可選
--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308
--
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