2.关于x的不等式mx2-(m+2)x+m+1>0解集为R,则实数m的取值范围是( )
| A. | m>$\frac{2\sqrt{3}}{3}$或m<-$\frac{2\sqrt{3}}{3}$ | B. | m<-$\frac{2\sqrt{3}}{3}$或m>0 | C. | m>$\frac{2\sqrt{3}}{3}$ | D. | m<-$\frac{2\sqrt{3}}{3}$ |
1.数列{an}中,a1=1,an=$\frac{{a}_{n-1}}{2{a}_{n-1}+1}$(n≥2),则a1009=( )
| A. | $\frac{1}{1009}$ | B. | $\frac{1}{2015}$ | C. | $\frac{1}{2016}$ | D. | $\frac{1}{2017}$ |
20.函数f(x)=2x+$\frac{3}{x}$(x>0)的最小值是( )
| A. | $\sqrt{6}$ | B. | 6 | C. | 2$\sqrt{6}$ | D. | $\frac{\sqrt{6}}{2}$ |
19.已知a>b>0,则下列结论中不正确的是( )
| A. | $\frac{1}{a}$<$\frac{1}{b}$ | B. | $\sqrt{\frac{{a}^{2}+{b}^{2}}{2}}$>$\frac{a+b}{2}$ | ||
| C. | $\root{3}{-a}$<$\root{3}{-b}$ | D. | log0.3$\frac{1}{a}$<log0.3$\frac{1}{b}$ |
18.已知|$\overrightarrow{a}$|=1,|$\overrightarrow{b}$|=2$\sqrt{3}$,|2$\overrightarrow{a}$-$\overrightarrow{b}$|=2$\sqrt{7}$,则向量$\overrightarrow{a}$与$\overrightarrow{b}$的夹角是( )
| A. | 150° | B. | 120° | C. | 60° | D. | 30° |
17.等比数列{an}是单调递增数列,且有a2a5=6,a3+a4=5,则其公比q=( )
| A. | $\frac{2}{3}$ | B. | $\frac{1}{5}$ | C. | 5 | D. | $\frac{3}{2}$ |
16.已知△ABC中,若b2+c2+$\sqrt{2}$bc=a2,则∠A=( )
| A. | 45° | B. | 60° | C. | 120° | D. | 135° |
15.等差数列{an}中,a7=12,则a3+a11=( )
| A. | 12 | B. | 24 | C. | 26 | D. | 168 |
14.数列{an}的前几项为$\frac{1}{7}$,$\frac{3}{77}$,$\frac{5}{777}$,$\frac{7}{7777}$…,则其通项公式为( )
| A. | an=$\frac{2n}{\frac{7}{9}(1{0}^{n}-1)}$ | B. | an=$\frac{18n-9}{7(1{0}^{n}-1)}$ | C. | an=$\frac{2n-1}{7(1{0}^{n}-1)}$ | D. | an=$\frac{2n-1}{\frac{7}{8}({8}^{n}-1)}$ |
13.向量$\overrightarrow{a}$=(2,-3),$\overrightarrow{b}$=(-4,x),且$\overrightarrow{a}$⊥$\overrightarrow{b}$,则x=( )
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| A. | $\frac{8}{3}$ | B. | -$\frac{8}{3}$ | C. | -6 | D. | 6 |