2022-2023學(xué)年河北省保定市唐縣一中高三(上)期中數(shù)學(xué)試卷
發(fā)布:2024/9/6 10:0:8
一、選擇題(每小題5分,共40分)
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1.已知數(shù)列{an}滿足an+1an+an-an+1+1=0,a102=-3,則( ?。?/h2>
組卷:41引用:2難度:0.7 -
2.已知正項(xiàng)等比數(shù)列{an}滿足a1=2,a4=2a2+a3,若設(shè)其公比為q,前n項(xiàng)和為Sn,則不正確的是( ?。?/h2>
組卷:18引用:2難度:0.7 -
3.已知正項(xiàng)等比數(shù)列{an},滿足a2?a72?a2020=16,則a1?a2…?a1017=( )
組卷:788引用:6難度:0.8 -
4.已知數(shù)列{an}滿足
,則a1=28,an+1-ann=2的最小值為( ?。?/h2>ann組卷:698引用:4難度:0.5 -
5.數(shù)列{an}滿足an+1=λan-1(n∈N*,λ∈R且λ≠0),若數(shù)列{an-1}是等比數(shù)列,則λ的值等于( ?。?/h2>
組卷:587引用:12難度:0.9 -
6.已知數(shù)列{bn}滿足b1=1,b2=4,
,則該數(shù)列的前23 項(xiàng)的和為( ?。?/h2>bn+2=(1+sin2nπ2)bn+cos2nπ2組卷:236引用:2難度:0.5 -
7.設(shè)Sn等差數(shù)列{an}的前n項(xiàng)和,且滿足S2018>0,S2019<0,對(duì)任意正整數(shù)n,都有|an|≥|ak|,則k的值為( )
組卷:84引用:4難度:0.6
四、解答題(共70分)
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21.已知橢圓E:
=1(a>b>0)的左、右焦點(diǎn)分別為F1,F(xiàn)2,焦距與短軸長(zhǎng)均為4.x2a2+y2b2
(1)求E的方程;
(2)設(shè)任意過(guò)F2的直線l交E于M,N,分別作E在點(diǎn)M,N處的切線,且兩條切線相交于點(diǎn)P,過(guò)F1作平行于l的直線分別交PM,PN于A,B,求的取值范圍.|OA+OB||OP|組卷:314引用:6難度:0.5 -
22.已知函數(shù)f(x)=ex-asinx-1在區(qū)間
內(nèi)有唯一極值點(diǎn)x1.(0,π2)
(1)求實(shí)數(shù)a的取值范圍;
(2)證明:f(x)在區(qū)間(0,π)內(nèi)有唯一零點(diǎn)x2,且x2<2x1.組卷:227引用:7難度:0.4