List of top Mathematics Questions on limits and derivatives asked in KCET

$$ \lim_{x \to 0} \frac{1 - \cos x}{x^2} = $$

$$ \lim_{x \to \infty} \left[ \frac{1^x + 2^x + 3^x + \cdots + n^x}{n} \right]^{1/x} = $$

The value of $\lim_{x \to 2} \frac{x^3 + 3x^2 - 9x - 2}{x^3 - x^2 - 4x + 4}$ is ________