設(shè)
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是二次函數(shù),方程
f(
x)=0有兩個相等的實根,且
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(1)求
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的表達(dá)式;
(2)求
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的圖象與兩坐標(biāo)軸所圍成圖形的面積.
(3)若直線x=-t(0<t<1)把y=f(x)的圖象與兩坐標(biāo)軸所圍成圖形的面積二等分,求t的值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本大題滿分12分)已知函數(shù)
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在R上有定義,對任何實數(shù)

和任何實數(shù)
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,都有
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(Ⅰ)證明
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;(Ⅱ)證明
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其中
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和
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均為常數(shù);
(Ⅲ)當(dāng)(Ⅱ)中的
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時,設(shè)
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,討論

在
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內(nèi)的單調(diào)性并求極值
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分14分)已知函數(shù)

有下列性質(zhì):“若
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,使得

”成立。
(1)利用這個性質(zhì)證明

唯一;
(2)設(shè)A、B、C是函數(shù)

圖象上三個不同的點(diǎn),試判斷△ABC的形狀,并說明理由。
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本題滿分14分)
已知函數(shù)
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,
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
,且

.
(Ⅰ)若

,求

的值;
(Ⅱ)當(dāng)

時,求函數(shù)

的最大值;
(Ⅲ)求函數(shù)

的單調(diào)遞增區(qū)間.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本題滿分14分)本題共有2個小題,第1小題滿分7分,第2小題滿分7分.
已知二次函數(shù)


對任意

均有
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成立,且函數(shù)的圖像過點(diǎn)


.
(1)求函數(shù)

的解析式;
(2)若不等式

的解集為

,求實數(shù)

的值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
設(shè)函數(shù)
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(1)當(dāng)
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時,求函數(shù)

的值域;
(2)若函數(shù)
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是(-
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,+

)上的減函數(shù),求實數(shù)

的取值范圍
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來源:不詳
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函數(shù)y=cos
2(2x+

)-sin
2(2x+

)的最小正周期是( )
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來源:不詳
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若函數(shù)

的零點(diǎn)有且只有一個,求

的值
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