List of top Mathematics Questions on Limits asked in BITSAT

Evaluate: \[ \lim_{x \to 0} \frac{\sin 3x - 3 \sin x}{x^3} \]

Let \( f(x) = \sin x \), \( g(x) = \cos x \), and \( h(x) = x^2 \). Then, evaluate: \[ \lim\limits_{x \to 1} \frac{f(g(h(x))) - f(g(h(1)))}{x - 1} \]