若質(zhì)點(diǎn)
M按規(guī)律
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運(yùn)動,則
t=2時(shí)的瞬時(shí)速度為( )
解:因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823220515344947.png" style="vertical-align:middle;" />,可見則t=2時(shí)的瞬時(shí)速度為4,選C
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(14分)已知定義在正實(shí)數(shù)集上的函數(shù)
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,
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,其中
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.設(shè)兩曲線
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,
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有公共點(diǎn),且在該點(diǎn)處的切線相同.
(1)用
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表示
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,并求

的最大值;
(2)判斷當(dāng)

時(shí),

的大小,并證明.
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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12分)
設(shè)函數(shù)

.
⑴ 當(dāng)
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時(shí),求函數(shù)

在點(diǎn)

處的切線方程;
⑵ 對任意的

函數(shù)

恒成立,求實(shí)數(shù)

的取值范圍.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
若函數(shù)

在定義域
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上恰有三個(gè)單調(diào)區(qū)間,則

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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12分)
已知函數(shù)

且導(dǎo)數(shù)

.
(1)試用含有

的式子表示

,并求

的單調(diào)區(qū)間;
(2)對于函數(shù)圖象上不同的兩點(diǎn)

,且

,如果在函數(shù)圖像上存在點(diǎn)

(其中

)使得點(diǎn)

處的切線

,則稱

存在“相依切線”.特別地,當(dāng)

時(shí),又稱

存在“中值相依切線”.試問:在函數(shù)

上是否存在兩點(diǎn)

使得它存在“中值相依切線”?若存在,求

的坐標(biāo),若不存在,請說明理由.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知函數(shù)
f(x)=x
2-
ax+b(a,b∈R)的圖像經(jīng)過坐標(biāo)原點(diǎn),且

,數(shù)列{

}的前n項(xiàng)和

=
f(n)(n∈N
*).
(Ⅰ)求數(shù)列{

}的通項(xiàng)公式;

(Ⅱ)若數(shù)列{

}滿足

+

=

,求數(shù)列{

}的前n項(xiàng)和.
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
已知函數(shù)

在

處的導(dǎo)數(shù)為-2,則
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
曲線
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在點(diǎn)(1,2)處的切線方程為
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
曲線

在點(diǎn)(0,1)處的切線方程為
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