If `L= lim_(xto0) (sin2x+asinx)/(x^(3))` is finite, then find the value of a and L.

Explanation

To solve the limit \( L = \lim_{x \to 0} \frac{\sin 2x + a \sin x}{x^3} \) and find the values of \( a \) and \( L \), we can follow these steps:

### Step 1: Rewrite the expression using trigonometric identities
We know that \( \sin 2x = 2 \sin x \cos x \). Therefore, we can rewrite the limit as:
\[ L = \lim_{x \to 0} \frac{2 \sin x \cos x + a \sin x}{x^3} \]

...