2.e为自然对数的底数,定义函数shx=$\frac{{e}^{x}-{e}^{-x}}{2}$,chx=$\frac{{e}^{x}+{e}^{-x}}{2}$,若已知函数f(x)为奇函数,且满足f(1)=ch1,当x>0时,f(x)+xf′(x)>shx,则f(x)<$\frac{chx}{x}$的解集为( )
| A. | (-∞,-1)∪(1,+∞) | B. | (-1,0)∪(0,1) | C. | (-1,0)∪(1,+∞) | D. | (-∞,-1)∪(0,1) |
1.已知$sin(α+\frac{π}{3})=\frac{1}{3}$,则$cos(\frac{π}{6}-α)$=( )
| A. | $-\frac{1}{3}$ | B. | $\frac{1}{3}$ | C. | $\frac{{2\sqrt{3}}}{3}$ | D. | $-\frac{{2\sqrt{3}}}{3}$ |
20.已知向量$\overrightarrow a$,$\overrightarrow b$的夹角为$\frac{π}{3}$,且$|{\overrightarrow a}|=1$,$|{\overrightarrow a+\overrightarrow b}|=\sqrt{7}$,则$|{\overrightarrow b}|$等于( )
| A. | 2 | B. | 3 | C. | $\sqrt{3}$ | D. | 4 |
16.焦点在y轴的椭圆x2+ky2=1的长轴长是短轴长的2倍,那么k等于( )
| A. | -4 | B. | $-\frac{1}{4}$ | C. | 4 | D. | $\frac{1}{4}$ |
15.
已知在直三棱柱ABC-A1B1C1中,∠ABC=90°,AB=BC=AA1=2,点D是A1C1的中点,则异面直线AD和BC1所成角的大小为( )
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| A. | $\frac{π}{6}$ | B. | $\frac{π}{3}$ | C. | $\frac{π}{4}$ | D. | $\frac{π}{2}$ |