3．设函数$y=y(x)$由$\left\{ \begin{matrix} x=t+{{\text{e}}^{t}}, \\ y={{t}^{2}}+{{\text{e}}^{t}} \\ \end{matrix} \right.$确定，则曲线$y=y(x)$在点$(1,1)$处的切线方程为()．
A. $y=\frac{1}{6}(x+5)$
B. $y=\frac{1}{4}(x+3)$
C. $y=\frac{1}{3}(x+2)$
D. $y=\frac{1}{2}(x+1)$
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4．函数$y={{x}^{\frac{1}{x}}}\ \ (x>0)$的单调递增区间为()．
A. $(\text{e},+\infty )$
B. $(0,\ \text{e})$
C. $(1,+\infty )$
D. $(0,\ 1)$
5．函数$f(x)={{\left| x \right|}^{\frac{2}{3}}}(x-1)$的极小值点为()．
A. $0$
B. $\frac{2}{5}$
C. $\frac{2}{3}$
D. $1$
2．$\int_{-\frac{1}{2}}^{\frac{1}{2}}{(2+x)\sqrt{1-4{{x}^{2}}}\text{d}x}=$()．
A. $\frac{\text{ }\!\!\pi\!\!\text{ }}{2}$
B. $\frac{\text{ }\!\!\pi\!\!\text{ }}{4}$
C. $0$
D. $-\frac{\text{ }\!\!\pi\!\!\text{ }}{4}$
7．$\int_{0}^{2}{\,\sin \left| x-1 \right|\text{d}x}=$()．
A. $0$
B. $1-\cos 1$
C. $2(1-\cos 1)$
D. $4(1-\cos 1)$
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