List of top Mathematics Questions on limits of trigonometric functions asked in MET

Let \( f(x) = \left[\frac{\sin x}{x}\right] + \left[\frac{2\sin x}{x}\right] + \cdots + \left[\frac{10\sin x}{x}\right] \) (where \([\,]\) is the greatest integer function). Find \( \lim_{x \to 0} f(x)\).

\(\lim_{x\to0} \frac{\sin3x - \sin x}{\sin x}\) is

The value of \(\lim_{\theta \to 0} \frac{\tan\theta}{\theta}\) is

The value of \( \lim_{x \to 0} \frac{1 - \cos x}{x^{2}} \) is: