Determine the values of `a ,\ b ,\ c` for which the function `f(x)={(sin(a+1)x+sinx)/x ,\ \ \ for\ x<0c ,\ \ \ for\ x=0(sqrt(x+b x^2))/(b x^(3//2)),\ \ \ for\ x >0` is continuous at `x=0`

Explanation

To determine the values of \( a \), \( b \), and \( c \) for which the function

\[
f(x) =
\begin{cases}
\frac{\sin((a+1)x) + \sin(x)}{x} & \text{for } x < 0 \\
c & \text{for } x = 0 \\
\frac{\sqrt{x + bx^2} - \sqrt{x}}{b x^{3/2}} & \text{for } x > 0
...