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

If \( f(x) = x^6 + 6^x \), then \( f'(x) \) is equal to

If \( f(x) = \sqrt{\frac{x - \sin x}{x + \cos^2 x}} \), then \( \lim_{x \to \infty} f(x) \) is equal to

If \( f:\mathbb{R} \to (0,\infty) \) is an increasing function and if \( \lim_{x \to 2018} \frac{f(3x)}{f(x)} = 1 \), then \( \lim_{x \to 2018} \frac{f(2x)}{f(x)} \) is equal to

If \( f \) is differentiable at \( x = 1 \), then \( \lim_{x \to 1} \frac{x^2 f(1) - f(x)}{x - 1} \) is

The limit \( \lim_{x\to0} \frac{\sqrt{2+x} - \sqrt{2-x}}{x} \) is equal to:

The value of $\lim_{n \to \infty} \frac{{}^nC_3 - {}^nP_3}{n^3}$ is equal to:

If \( f(x) = 3x^2 - 7x + 5 \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \) is equal to

\[ \lim_{x \to \infty} \left(\frac{x^2}{3x-2} - \frac{x}{3}\right) \]

The value of $\displaystyle \lim_{y \to \infty} \left[ y \sin\left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to}

If $ f(x)=(x-2)(x-4)(x-6)....(x-2n), $ then $ f'(2) $ is