For small values of x, sin(x) is approximately equal to x. Since the limit is approaching to a smaller value, we can assume this. The approximation "x 
sin(x) for small values of x" is a useful estimation tool.
Now, limx->0 x log(sin x) = limx->0 x log(x) = limx->0 (log(x) / (1/x)). Now as x approaches to 0, log(x) approaches to infinity and (1/x) too approaches to infinity (easily seen if we plot the graph). Therefore we can apply l'Hospital rule as it's a (∞/∞) form.
Differentiating numerator and denominator, we get finally (-x / ln 10). Putting limit to it, we get 0 as the answer.
Option (a)
