List of top Mathematics Questions on Limit and Continuity asked in MHT CET

Find the value of \(k\) if the function \(f(x)=\dfrac{k\sin x}{x}\) for \(x\neq0\) and \(f(0)=3\) is continuous at \(x=0\).

Evaluate the limit: \[ \lim_{n \to \infty} \left[ \frac{1}{1 - \pi} + \frac{8}{1 + \pi} + \cdots + \frac{x^2}{n\pi} \right]. \]