f(x) = \(\begin{cases}\frac{sin(a + 1)x + sinx}{x}, & x < 0\\c,& x = 0\\ \frac{\sqrt{x + bx^2}- \sqrt x}{bx\sqrt x}, &x > 0\end{cases}\)

Question

Find a, b, c if the function

f(x) = \(\begin{cases} \frac{sin(a + 1)x + sinx}{x}, & x < 0\\c,& x = 0\\ \frac{\sqrt{x + bx^2} - \sqrt x}{bx\sqrt x}, &x > 0 \end{cases}\)  is continuous at x = 0.

Answer 1

At x = 0, given function is continuous then,