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A function f(x) is said to be continuous in an open interval (a, b), if it is continuous at every point in this interval.
A function f(x) is said to be continuous in the closed interval [a, b), if f(x) is continuous in (a, b) and $\lim\limits_{\text{x}\rightarrow0}\text{f}(\text{a}+\text{h})=\text{f}(\text{a})$ and $\lim\limits_{\text{x}\rightarrow0}\text{f}(\text{b}-\text{h})=\text{f}(\text{b})$
If function $\text{f}(\text{x})=\begin{cases}\frac{\sin(\text{a}+1)\text{x}+\sin\text{x}}{\text{x}}&,\text{x}<0\\\text{c}&,\text{x}=0\\\frac{\sqrt{\text{x}+\text{bx}^2}-\sqrt{\text{x}}}{\text{bx}^{\frac{3}{2}}}&,\text{x}>0\end{cases}$ is continuous at x = 0, then answer the following questions.

1. The value of a is:

1. $-\frac{3}{2}$
   
2. $0$
   
3. $\frac{1}{2}$
   
4. $-\frac{1}{2}$
   

2. The value of b is:

1. 1
2. -1
3. 0
4. Any real number.

3. The value of c is:

1. $1$
   
2. $\frac{1}{2}$
   
3. $-1$
   
4. $-\frac{1}{2}$
   

4. The value of a + c is:

1. 1
2. 0
3. -1
4. -2

5. The value of c - a is:

1. 1
2. 0
3. -1
4. 2