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 ________

$\displaystyle\lim_{x \to 0} \frac{xe^x - \sin \, x}{x}$ is equal to

If the function $f(x)$ defined by $\frac {x^{100}}{100}+\frac {x^{99}}{100}+\dots \frac {x^2}{100}+x+1$ then $f'(0)$ is equal to

$ \displaystyle\lim _{n \rightarrow \infty} n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}$ is