19.如果f(x)=$\frac{1}{2}$(m-2)x2+(n-8)x+1(m>2,n>0)在[$\frac{1}{2},2$]上单调递减,则$\frac{1}{m}$+$\frac{1}{n}$的最小值为( )
A. | $\frac{\sqrt{2}}{3}$ | B. | $\frac{\sqrt{2}}{6}$ | C. | $\frac{3+2\sqrt{2}}{12}$ | D. | $\frac{3-2\sqrt{2}}{12}$ |
18.若实数x,y满足条件$\left\{\begin{array}{l}{x-y+1≥0}\\{x+y≥2}\\{x≤1}\end{array}\right.$,则2x+y的最大值为( )
A. | 5 | B. | 4 | C. | 3 | D. | $\frac{5}{2}$ |
17.△ABC中,角A,B,C所对的边分别为a,b,c,其面积S=a2-(b-c)2,则tan$\frac{A}{2}$=( )
A. | $\frac{1}{2}$ | B. | $\frac{1}{3}$ | C. | $\frac{1}{4}$ | D. | $\frac{1}{6}$ |
16.已知△ABC的两边长分别为2,3,这两边的夹角的余弦值为$\frac{1}{3}$,则△ABC的外接圆的直径为( )
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A. | $\frac{9\sqrt{2}}{2}$ | B. | $\frac{9\sqrt{2}}{4}$ | C. | $\frac{9\sqrt{2}}{6}$ | D. | 8$\sqrt{2}$ |