8．设$a>0$，则$\int_{0}^{a}{\frac{\text{d}x}{x+\sqrt{{{a}^{2}}-{{x}^{2}}}}}=$()．
A. $\frac{\text{ }\!\!\pi\!\!\text{ }}{2}$
B. $\frac{\text{ }\!\!\pi\!\!\text{ }}{4}$
C. $\frac{\text{ }\!\!\pi\!\!\text{ }}{6}$
D. $\frac{\text{ }\!\!\pi\!\!\text{ }}{8}$
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9．$\int_{0}^{1}{\frac{2x}{(x+1){{({{x}^{2}}+1)}^{2}}}\text{d}x}=$()．
A. $\frac{1\text{+}\ln 2}{2}$
B. $\frac{1\text{+}\ln 2}{4}$
C. $\frac{1}{2}+\frac{\ln 2}{4}$
D. $\frac{1}{2}-\frac{\ln 2}{4}$
10．从原点向曲线$y=1-\ln x$作切线，则由切线、曲线和$x$轴围成图形的面积为()．
A. $\frac{1}{2}{{\text{e}}^{2}}+\text{e}$
B. $\frac{1}{2}{{\text{e}}^{2}}-\text{e}$
C. ${{\text{e}}^{2}}+\text{e}$
D. ${{\text{e}}^{2}}-\text{e}$
2．若幂级数$\sum\limits_{n=0}^{\infty }{{{a}_{n}}{{(x-1)}^{2n}}}$在$x=2$处条件收敛，则下列结论中错误的是()．
A. $\sum\limits_{n=0}^{\infty }{{{a}_{n}}{{(x-1)}^{2n}}}$的收敛半径为$1$
B. $\sum\limits_{n=0}^{\infty }{{{a}_{n}}{{(x-1)}^{2n}}}$的收敛域为$[0,2]$
C. 数项级数$\sum\limits_{n=0}^{\infty }{{{a}_{n}}}$收敛
D. 数项级数$\sum\limits_{n=0}^{\infty }{{{(-1)}^{n}}{{a}_{n}}}$收敛
3．设常数$\alpha >0$，正项级数$\sum\limits_{n=1}^{\infty }{{{a}_{n}}}$收敛，则级数$\sum\limits_{n=1}^{\infty }{{{(-1)}^{n}}\frac{\sqrt{{{a}_{2n-1}}}}{\sqrt{{{n}^{2}}+\alpha }}}$()．
A. 发散
B. 条件收敛
C. 绝对收敛
D. 敛散性与$\alpha $的值有关
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