List of top Mathematics Questions on limits and derivatives asked in AP EAPCET

The value of the limit $\lim_{x \to 0} \frac{e^{3x} - e^{-2x}}{\sin 4x}$ is:

The value of the limit \( \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \) is equal to:

The value of the limit $\lim_{x \to 0} \frac{e^{3x} - e^{-2x}}{\sin 4x}$ is:

The value of $\lim_{x \to \infty} \left(\frac{x+6}{x+1}\right)^{x+4}$ is:

Let \[ f(x)=\lim_{y\to\infty} y\left(x^{1/y}-1\right), \] and \[ 2022\,f\left(\frac{1}{x}\right)+P\,f(x)=f(x^2), \] then \(P=\)

If \([\,]\) denotes the greatest integer function, then \[ \lim_{x\to \frac{\pi}{2}^{+}} \frac{[\sin x]-[\cos x]+1}{2} = \]

If \(A\neq 0\) and \(x>0\), then \[ \lim_{n\to\infty} \frac{\cos x-e^{-nx}} {1-Ae^{-nx}} = \]

Which of the following is divisible by $x^{2}-y^{2}, \forall x\ne y$?